Why Is Binary Used in Electronics and Computers?

Why is binary used in electronics? Geralt via Pixabay.com

Why Do Computers Use Binary?

The binary numbering system is the basis for the storage, transfer and manipulation of data in computer systems and digital electronic devices. This system uses base 2 rather than base 10, which is what we are familiar with for counting in everyday life. By the end of this easy-to-understand article, you'll have a grasp of why binary is used in computers and electronics.

What Is Decimal and Why Do We Use It?

Before we learn about binary, let's start with decimal.

The decimal, base 10 or denary numbering system is what we are familiar with in everyday life. It uses 10 symbols or numerals. To count, we go:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ...

... But there's no numeral for the next number, the integer value we interpret as "ten". Ten is therefore represented by two digits: the numeral 1 followed by 0, so ten is represented as "10", which really means "one ten and no units". Similarly, one hundred is represented by three digits: 1, 0 and 0; i.e., one hundred, no tens and no units".

Basically, numbers are represented by a series of numerals in the units, tens, hundreds, thousands place etc. For instance, 134 means one hundred, three tens and four units. The decimal system probably arose because we have 10 fingers on our hands, which could be used for counting.

Public domain image via Pixabay

What Is Binary and How Does It Work?

The binary system used by computers is based on two numerals: 0 and 1. So you count:

0, 1

... But there's no numeral for 2. So 2 is represented by 10 or "one 2 and no units". In the same way that there is a units, tens, hundreds, and thousands place in the decimal system, in the binary system, there is a units, twos, fours, eights, sixteens place etc. in the binary system. So the binary and decimal equivalents are as below:

• 00000000 = 0
• 00000001 = 1
• 00000010 = 2
• 00000011 = 3
• 00000100 = 4
• 00000101 = 5
• 00000110 = 6
• 00000111 = 7 (and so on)

Counting in binary from 0 to 11111 = 31 decimal. Ephert, CC by SA 4.0 via Wikimedia Commons

A printed circuit board (PCB) with digital integrated circuits (ICs or "chips"). Olafpictures, public domain image via Pixabay.com

Why Do Computers Use Binary?

"A single switch can be on or off, enabling the storage of 1 bit of information. Switches can be grouped together to store larger numbers. This is the key reason why binary is used in digital systems."

How Is Binary Used in Digital Computers and Electronic Devices?

Numbers can be encoded in binary format and stored using switches. The digital technology which uses this system could be a computer, calculator, digital TV decoder box, cell phone, burglar alarm, watch etc. Values are stored in binary format in memory, which is basically a bunch of electronic on/off switches.

Imagine if you had a bank of 8 rocker switches, just like in the image below. Each switch could represent 1 or 0, depending on whether it is turned on or off. So you think of a number and set the switches on or off to "store" the binary value of this number. If someone else then looked at the switches, they could "read" the number.

8 bit “memory” made from a gang of rocker switches. Conceptual idea of how the state of a bank of eight switches allows the "storage" of 2 to the power of 8 = 256 possible numbers. © Eugene Brennan

How Does a Computer Implement Switches

So how does a computer store binary numbers? Obviously, banks of rocker switches would be ridiculously impractical (although a similar technique was used in early computers when programming) In a computer, switches are implemented using microminiature transistors.

The smallest memory configuration is the bit, which can be implemented with one switch. If 8 switches are added together, you get a byte. The digital hardware is able to set the switches on and off (i.e. write data to a byte) and also read the state of the switches. In the conceptual image of rocker switches we saw above, there are 8 switches and 2⁸ = 256 permutations or arrangements depending on whether a switch is on or off. If on represents 1 and off represents 0 for each switch, the group of switches can represent any of the following values.

• 00000000 0 decimal
• 00000001 1 decimal
• 00000010 2 decimal
• 00000011 3 decimal
• 00000100 4 decimal
• ...
• 11111110 254 decimal
• 11111111 255 decimal

In an electronic device or computer, because of micro-miniaturisation, billions of switches can be incorporated into integrated circuits (IC), potentially allowing the storage and manipulation of huge amounts of information.

Binary and Decimal Equivalents

Binary and Decimal Equivalents

Binary	Decimal
0	0
1	1
10	2
11	3
100	4
101	5
110	6
111	7
1000	8
1001	9
1010	10
1011	11
1100	12
1101	13
1110	14
1111	15
10000	16

Representing Non-Integer Values in Computer Systems

Integers can be stored and processed directly as their binary equivalents in computer systems; however, this isn't the case with other data. A machine such as a computer, digital camera, scanner etc., cannot directly store decimals, non-numerical (text, image, video) or analogue measurement data from the real world directly. This type of data could be:

• Person's name or address
• Temperature measured in a room
• Image from a digital camera or scanner.
• Audio
• Video
• Decimal number

Representing Data in Floating Point Format

Decimal numbers are represented in computer systems using a system known as floating point. A decimal number can be represented approximately, to a certain level of accuracy by an integer significand multiplied by a base, raised to the power of an integer exponent.

Processing and Storage of Analogue Data

A voltage level from a temperature sensor is an analogue signal and has to be converted to a binary number by a device called an analogue-to-digital converter (ADC). These devices can have various resolutions, and for a 16 bit converter, the signal level is represented by a number from 0 to 2¹⁶ = 65535. ADCs are also used in image scanners and digital cameras—electronic equipment used to record sound and video and basically any digital device that takes input from a sensor. An ADC converts a real-world analogue signal into data that can be stored in memory. Images created in a CAD drawing package are also broken down into individual pixels, and a byte of data is used for the red, green and blue intensity levels of each pixel.

Digital signals in electronic circuitry are either high or low, representing a "1" or "0". © Eugene Brennan

Encoding Text Data as ASCII

Names, addresses or other text entered into a computer can't be stored directly in computer memory. Instead the text is broken down into individual letters, numerals and other non alphanumeric characters (e.g., &*£$# etc) and a coding system called ASCII represents each character by a number from 0 to 127. This data is then stored in binary format as one or more bytes in memory, each byte being made up of individual bits, and each bit implemented using transistors.

ASCII Table Hex, Binary and Decimal Values

Table showing ASCII characters with their hexadecimal, binary and decimal values. Hexadecimal or "hex" is a convenient way of representing a byte or word of data. Two characters can represent 1 byte of data.

ASCII code table. ASCII assigns a number from 0 to 127 to letters, numbers, non alphanumeric characters and control codes. Public domain image via Wikimedia Commons

What Is Machine Code and Assembly Language?

Not only are values or data stored in memory, but also the instructions which tell the microprocessor what to do. These instructions are called machine code. When a software program is written in a high level language such as BASIC, Java or "C", another program called a compiler breaks the program down into a set of basic instructions called machine code. Each machine code number has a unique function which is understood by the microprocessor. At this low level, instructions are basic arithmetic functions such as add, subtract and multiply involving the contents of memory locations and registers (a cell which can have arithmetic operations carried out on it). A programmer can also write code in assembly language. This is a low level language comprising instructions known as mnemonics which are used to move data between registers and memory and perform arithmetic operations.

How to Convert Decimal to Binary and Binary to Decimal

This tutorial explains how to convert decimal to binary and binary to decimal.

George Boole and Boolean Algebra

Boolean algebra, developed by the British mathematician George Boole in the 19th century, is a branch of mathematics which deals with variables which can only have one of two states, true or false. In the 1930s, Boole's work was discovered by the mathematician and engineer Claude Shannon, who realised it could be used to simplify the design of telephone switching circuits. These circuits originally used relays which could be either on or off, and the desired output state of the system, depending on the combination of states of the inputs, could be described by a Boolean algebraic expression. Boolean algebra rules could then be used to simplify the expression, resulting in a reduction of the number of relays required to implement a switching circuit. Eventually Boolean algebra was applied to the design of digital electronic circuitry as we will see below.

Digital Logic Gates: AND, OR and NOT

A digital state, ie high/low or 1/0 can be stored in a one-bit cell in memory, but what if that data has to be processed? The most basic processing element in a digital electronic circuit or computer is a gate. A gate takes one or more digital signals and generates an output. There are three types of gates: AND, OR and NOT (INVERT). In their simplest form, small groups of gates are available on a single IC. However, a complex combinational logical function can be implemented using a Programmable Logic Array (PLA) and more sophisticated devices such as microprocessors are composed of millions of gates and memory storage cells.

• For an AND gate, the output is true or high only when both inputs are true.
• For an OR gate, the output is high if either or both inputs are true.
• For a NOT gate or inverter, the output is the opposite state to the input.

Boolean algebraic expressions can be used to express what the output signal of a circuit should be, depending on the combination of inputs. The main operations in Boolean algebra are and, or and not. During a design process, the required value of an output for all the various permutations of input states can be tabulated in a truth table. The value '1' in the truth table means an input/output is true or high. The value '0' means the input/output is false or low. Once a truth table is created, a Boolean expression can be written for the output, simplified and implemented using a collection of logic gates.

So a typical Boolean expression with three independent variables A, B and C and one dependent variable D would be:

Y = A.B + C

This is read as "Y = (A and B) or C"

Logic gates, AND, OR and NOT and their truth tables. © Eugene Brennan

Truth table for a simple digital circuit. Y = A.B + C © Eugene Brennan

Disclaimer

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualised advice from a qualified professional.

© 2012 Eugene Brennan

How to Convert Decimal to Binary and Binary to Decimal

Base 2, the Basis for Binary Code

The base 2, or binary numbering system is the basis for all binary code and data storage in computing systems and electronic devices. This guide shows you how to convert from binary to decimal and decimal to binary.

Binary number and its decimal equivalent. © Eugene Brennan

Decimal, the Base 10 Numbering System

First let's start with decimal.

The decimal, also known as the denary or base 10 numbering system is what we use in everyday life for counting. The fact that there are ten symbols is more than likely because we have 10 fingers.

We use ten different symbols or numerals to represent the numbers from zero to nine.

Those numerals are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

When we get to the number ten, we have no numeral to represent this value, so it is written as:

10

The idea is to use a new place holder for each power of 10 to make up any number we want.

So 134 really means one hundred, 3 tens and 4 units, although we just interpret and read it as the number one hundred and thirty four.

Placeholder Value in the Decimal Numbering System

Placeholder value in the base 10 number system. © Eugene Brennan

Binary, the Base 2 Numbering System

In the decimal number system, we saw that ten numerals were used to represent numbers from zero to nine.

Binary only uses two numerals 0 and 1. Place holders in binary each have a value of powers of 2. So the first place has a value 2⁰ = 1, the second place 2¹ = 2, the third place 2² = 4, the fourth place 2³ = 8 and so on.

In binary we count 0, 1 and then since there's no numeral for two we move onto the next place holder so two is written as 10 binary. This is exactly the same as when we get to ten decimal and have to write it as 10 because there's no numeral for ten.

Placeholder Value in the Binary Numbering System

Placeholder value in the binary number system. © Eugene Brennan

Most Significant Bit (MSB) and Least Significant Bit (LSB)

Most significant bit (MSB) and least significant bit (LSB). © Eugene Brennan

For a binary number, the most significant bit (MSB) is the digit furthermost to the left of the number and the least significant bit (LSB) is the rightmost digit.

Decimal and Binary Equivalents

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000

Steps to Convert from Decimal to Binary

If you don't have a calculator to hand, you can easily convert a decimal number to binary using the remainder method. This involves dividing the number by 2 recursively until you're left with 0, while taking note of each remainder.

1. Write down the decimal number.
2. Divide the number by 2.
3. Write the result underneath.
4. Write the remainder on the right hand side. This will be 0 or 1.
5. Divide the result of the division by 2 and again write down the remainder.
6. Continue dividing and writing down remainders until the result of the division is 0.
7. The most significant bit (MSB) is at the bottom of the column of remainders and the least significant bit (LSB) is at the top.
8. Read the series of 1s and 0s on the right from the bottom up. This is the binary equivalent of the decimal number.

Converting decimal to binary. © Eugene Brennan

Steps to Convert Binary to Decimal

Converting from binary to decimal involves multiplying the value of each digit (i.e. 1 or 0) by the value of the placeholder in the number

1. Write down the number.
2. Starting with the LSB, multiply the digit by the value of the place holder.
3. Continue doing this until you reach the MSB.
4. Add the results together.

Converting binary to decimal. © Eugene Brennan

Test Yourself!

1. What is 548 in binary?
2. What is 101011001 in decimal?
3. What is 01010101 in decimal?

Answers at bottom of page

Indicating the Base of a Number

The binary number 1011011 can be written as 1011011₂ to explicitly indicate the base. Similarly 54 base 10 can be written 54₁₀ Often however, the subscript is omitted to avoid excessive detail when the context is known. Usually subscripts are only included in explanatory text or notes in code to avoid confusion if several numbers with different bases are used together.

What is Binary Used For?

For more details on how binary is used in computer systems and digital electronics, see my other article:

Why is Binary Used In Computers and Electronics?

What Other Bases Are There Apart From 2 and 10?

Base 16 or hexadecimal (hex for short) is a shorthand used when programming computer systems. It uses sixteen symbols, representing 10, 11, 12, 13, 14 and 15 decimal with the letters A, B, C, D, E, and F respectively. You can read more about converting hex to binary and binary to hex here:

How to Convert Hex to Binary and Binary to Hexadecimal

Answers to Problems

1. 548 decimal is 1000100100 binary
2. 101011001 is 345 decimal
3. 01010101 is 85 decimal

© 2018 Eugene Brennan

How to Convert Hex to Binary and Binary to Hexadecimal

The Hexadecimal Numbering System

The base 16, also known as hexadecimal (abbreviated to hex) numbering system is regularly used in computer coding for conveniently representing a byte or word of data. This guide shows you how to convert from hex to binary and binary to hexadecimal.

© Eugene Brennan

Decimal, the Base 10 Numbering System

Before we learn how to convert hex to binary, let's try and understand how the base 10 system works.

The decimal, also known as the denary or base 10 numbering system that we use in everyday life makes use of ten symbols or numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

So to count you start with 0, then continue 1...2...3...4...5...6...7...8...9

What happens when you get to ten? There's no numeral for ten, so it's represented as

10

Which means 1 ten and no units

Similarly when you get to 99, there's no numeral for one hundred, so you write one hundred as 100.

So writing a number in the base 10 system involves using numerals in a "units", "tens", "hundreds", "thousands" place and so on

So 145 really means "one hundred, 4 tens and 5 units" although we just think of it as the number one hundred and forty five.

Hexadecimal, the Base 16 Numbering System

Hexadecimal or "hex" is a numbering system which uses 16 different numerals. We saw that decimal used ten numerals from 0 to 9. Hex expands on this by adding six more—the capital letters A, B, C, D, E and F.

So to count from 0 to 9 you go 0...1...2...3...4...5...6...7...8...9

But what happens next?

Simply continue with A...B...C...D...E...F which represents 10, 11, 12, 13, 14 and 15 decimal.

So now to count to 15 we go 0...1...2...3...4...5...6...7...8...9...A...B...C...D...E...F

In the decimal system, we saw that when we got to nine, there was no numeral for ten so it was represented as 10 or "one ten and no units".

In the hex system when we get to F which is 15 decimal, we have to represent the next number sixteen as 10 or "one 16 and no units".

Binary, the Base 2 Numbering System

The binary system used by computers is based on 2 numerals; 0 and 1. So you count 0, 1, there is no numeral for 2, so 2 is represented by 10 or "one 2 and no units". In the same way that there is a units, tens, hundreds, thousands place in the decimal system, in the binary system there is a units, twos, fours, eights, sixteens place etc. in the binary system.

Decimal to Hex and Binary Table

Binary, decimal and hex equivalents.

Decimal	Hex	Binary
0	0	0
1	1	1
2	2	10
3	3	11
4	4	100
5	5	101
6	6	110
7	7	111
8	8	1000
9	9	1001
10	A	1010
11	B	1011
12	C	1100
13	D	1101
14	E	1110
15	F	1111
16	10	10000
17	11	10001
18	12	10010
19	13	10011
20	14	10100
...	...	...
25	19	11001
26	1A	11010
27	1B	11011
28	1C	11100
29	1D	11101
30	1E	11110
31	1F	11111
32	20	100000
33	21	100001
34	22	100010

Indicating the Base of a Number

If a number isn't decimal (base 10), the base can be explicitly indicated by a subscript to avoid confusion. Sometimes the subscript is omitted to avoid excessive detail if the base has been specified earlier in a discussion or if numbers are listed in a table (e.g. numbers may be indicated as hex in the title of the table).

So for instance 1F hex (31 decimal) can be written 1F₁₆

Steps to Convert Hex to Binary

Hex is very easy to convert to binary.

1. Write down the hex number and represent each hex digit by its binary equivalent number from the table above.
2. Use 4 digits and add insignificant leading zeros if the binary number has less than 4 digits. E.g. Write 10₂ (2 decimal) as 0010_2.
3. Then concatenate or string all the digits together.
4. Discard any leading zeros at the left of the binary number.

© Eugene Brennan

Most Significant Bit (MSB) and Least Significant Bit (LSB)

For a binary number, the most significant bit (MSB) is the digit furthermost to the left of the number and the least significant bit (LSB) is the rightmost digit.

© Eugene Brennan

Steps to Convert Binary to Hex

Binary is also easy to convert to hex.

1. Start from the least significant bit (LSB) at the right of the binary number and divide it up into groups of 4 digits. (4 digital bits is called a "nibble").
2. Convert each group of 4 binary digits to its equivalent hex value (see table above).
3. Concatenate the results together, giving the total hex number.

© Eugene Brennan

Test Yourself!

For each question, choose the best answer. The answer key is below.

1. Convert ABCD hex to binary
   • 10101010
   • 1010101111001101
   • 1111111011001101
   • 1111000011101010
2. What is 10101010 in hex?
   • AA
   • FF
   • FD
   • 1010
3. Convert FFFF to decimal
   • 15151515
   • 255255
   • 65,535
   • 3125

Answer Key

1. 1010101111001101
2. AA
3. 65,535

What is Hex Used For?

Because of the ease of converting from hex to binary and vice versa, it's a convenient shorthand for representing byte values i.e. numbers from 0 to 255. Also it is compact, requiring only 2 digits for a byte and 4 digits for a word.

Typical uses of hex:

• Hex dumps are listings of the bytes in a file in hex format. Because decimal or binary numbers can be displayed compactly as pairs or multiple pairs of digits or characters from A to F, values line up in columns and are easy to trace through.
• Assembly language is written as a series of mnemonic (short, easy to remember word) instructions for a microprocessor. The operand (the data operated on by an opcode) is commonly specified as a hex value. It's also used to indicate the storage location of data

Example of assembly language instruction

In the short code segment below, MOV is the opcode (instruction) and 61 hex is the operand that the opcode acts on. AL is a register that stores a value temporarily so that arithmetic can be done on it before it's moved to memory. A program called an assembler converts the human understandable assembly language to machine code.

MOV AL, 61H ; Load AL register with 61 hex (97 decimal )

Assembly Language Program for an 8 Bit Microprocessor

Original image public domain via Wikimedia Commons

Hex Dump of a File

A "hex dump" or byte value listing of a JPG file as viewed in a file editor. On the left, each byte is displayed as a hex value. On the right, alphanumeric characters corresponding to ASCII values of the bytes are shown. © Eugene Brennan

ASCII Code Table

Two hex numerals also conveniently represent the 255 codes of the extended ASCII character set, used in computing for communication and text storage and display. Yuriy Arabskyy, CC-SA-3.0 via Wikimedia Commons

How to Convert Decimal to Binary

To convert decimal to binary and binary to decimal, see my other guide:
How to Convert Decimal to Binary and Binary to Decimal

What is Binary Used For?

For more details on how binary is used in computer systems and digital electronics, see my other article:

Why is Binary Used In Computers and Electronics?

How to Convert Hex to Decimal

You can convert hex to decimal by simply multiplying each hex numeral by the placeholder's value as a power of 16 and adding the result. (F₁₆ = 15 decimal and A₁₆ = 10 decimal)

Example: What is the decimal equivalent of 52FA₁₆ ?

52FA₁₆ = 5 x 16³ + 2 x 16² + 15 x 16¹ + 10 x 16⁰

= 5 x 4096 + 2 x 256 + 15 x 16 + 10 x 1

= 21,242

This article is accurate and true to the best of the author’s knowledge. Content is for informational or entertainment purposes only and does not substitute for personal counsel or professional advice in business, financial, legal, or technical matters.

© 2018 Eugene Brennan

The Andromeda Galaxy: "It's Big, And Also Faaarrr Away"

The apparent size of the Andromeda Galaxy, compared to that of the Moon. AI image created by Grok.

At a distance of 2.5 million light-years, or 24 million trillion km, the Andromeda Galaxy is the most distant object visible to the naked eye. We can see it because space is mostly empty, and light from the stellar object reaches us relatively unchanged, unlike what happens when we view distant objects on the horizon on Earth. Mountains, for instance, sometimes appear bluish and less distinct, or even invisible. That's because moisture in the air scatters and absorbs the light as it makes its way to our eyes.
The Andromeda Galaxy is incredibly distant. To paraphrase Father Ted Crilly, "It's big, and also faaarrr away." So even though it is far away, the fact that it's hundreds of thousands of light years in diameter makes it appear large in the night sky. That's when imaged with a long exposure through a telescope. In fact, it's about six times the apparent width of the Moon, but very faint. You can only see it out of the corner of your eye as a faint, fuzzy patch, and what you are seeing is the bright central bulge. The galaxy appears elliptical because, although it's actually a spiral galaxy with spiral arms, it's tilted at an angle of about 77° to the plane of the Milky Way.
 

Loading Data for the Kilcullen 38 kV Substation.

Loading data for the Kilcullen 38 kV Substation, courtesy ESB Networks.

From the ESB Networks document 38 kV & 110 kV Station Special Load Readings. 

The table shows summer and winter loads in megawatt (MW) for transformers T41, T42 and T424.

MVA is megavolt-ampere, often seen quoted on generators, although domestic generators are usually rated in kVA (kilovolt-ampere). The base unit, the volt-amp (VA) is a measure of apparent power and is the product of volts and amps sourced or used. In AC equipment, not all of that apparent power is used, and real power is measured in watts (W), which is the product of volts and in-phase current. ESB Networks want us to use in-phase current, and the extent to which current is in-phase with voltage is given by the power factor of a load. Non-in-phase currents waste power in supply cables, so power-factor correction may be implemented. This is normally done for large loads such as motors in industrial settings, although domestic fluorescent lighting may also include power factor correction in the fittings to compensate for the inductive load caused by the ballast coils (known as inductors). The correction can simply be a component called a capacitor wired in parallel with the light, inside the housing.

More information here on how Kilcullen gets its power.

Data courtesy ESB Networks.

It Came From Outer Space....

Nostoc commune (Latin name), also known as "jelly fungus". © Eugene Brennan

 Well not quite. This is probably Nostoc commune (Latin name), also known as "jelly fungus", "star jelly" or "witch's butter". It's not actually a fungus, but a colony of bacteria. There's loads of it in a patch on my yard, but it sometimes grows on lawns. It's extremely slippery on a lawn. Apparently it's eaten as a salad in the Philippines when dried out. I'm a fussy eater so I won't be trying it anytime soon.

More information on jelly fungus here on Wikipedia.

Off-Road Lanes for Cycling in Kildare and Wicklow

Lane from Barretstown to Bishopshill Commons. © Eugene Brennan

I'm always on the lookout for new trails and farm lanes for cycling on. Some are marked with a cul-de-sac sign, and just end up at farmhouses. However, others actually link two roads. Usually, there’s no sign at the junction where they meet a main road, or even a road number, so it can be a mystery where they go. The best way to work out whether there's a through route is to check old maps and Google satellite imagery. (The road layer of Google Maps sometimes only shows sections of a lane). I've found around six of them in the Kildare/Wicklow area. This is one of my favourite trails that runs between the Ballymore Eustace–Barretstown Castle road and the Ballymore–Bishopshill road. (The back road to Blessington which runs at the rear of the Russborough House estate.) It's only really passable in dry weather, as like many of these lanes, it gets flooded at several points and it's  necessary to climb up into the ditch through briars to avoid the floods. Also the ground on such lanes can be hard going as the surfaces are usually untarmacked, potholed and sometimes the surface is churned up by horses' hooves. The screenshot map at the end of this post shows a Google My Map I created. You can zoom into the map when you visit it at this link, or by following the link in the map's caption.

The ground that this trail passes over is hilly and rocky. Looking at the Geological Survey Ireland bedrock map, it appears that the rock in this area is slate and greywacke. The formations here are called the "Glending Formation" and the "Slate Formation". Greywacke is currently quarried north of Blessington near Rathmore and slate was also extracted at least as far back as the early-19th century, resulting in the townland being named "Slate Quarries".

Bedrock geology in the vicinity of Barretstown. Contains Irish Public Sector Data (Geological Survey Ireland) licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence

 

Some nice off-road cycling routes. Image courtesy Google Maps.

Available Substation Capacity in Ireland

Information on substations. Image courtesy ESB Networks.

This interesting interactive map on the ESB Networks website shows transformer capacities. A "substation" indicated on the map could be an actual town substation like the one at Sunnyhill, with 1, 2 or more transformers and associated switchgear and circuit breakers, or a transformer in a cabinet or small building (common in the newer housing estates). A substation could also be a pole transformer. Demand Firm Capacity (DFC) is a measure of a substation's redundancy guaranteed supply available under a "single contingency" (fault). So while named capacity is the total output of a substation, (e.g. 2 MVA for a substation with two, 1 MVA transformers)., DFC is the max output with one of the transformers out of action.

Demand Capacity Available is the amount of spare VA capacity for connections.

In the first image, the popup shows the status for the substation beside Nolan's car park.

In the second image below, the spec is given for Kilcullen 38 kV Station at Sunnyhill. (ESB Networks have it in the wrong place. They haven't fixed it since I let them know). It has two 5 MVA transformers and one 10 MVA transformer. Demand Firm Capacity is 18 MVA. That's based on the larger transformer going off line. That leaves 2 x 5MVA = 10 MVA. The 18 MVA DFC assumes that it takes time for cooling oil to heat up, so a transformer can take higher loads and give overcapacity for a period of several hours until a fault is repaired.

Only 0.6 MVA or 600 kVA Demand Capacity Available is indicated for the town's substation. Also there's a Demand Parent Constraint from the substation's parent at Stratford.

This is a link to the ESB Networks available capacity heatmap.

View the Distribution Network Development Plan.

Information on substations. Image courtesy ESB Networks.

What Is the Ground Wire For?

© Eugene Brennan

What Is a Ground Wire?

The hot and neutral cores in a power cable are used to supply current to the appliances in your home. So what about the green wire? Why is it needed? This is known as the "ground" and is an additional wire that is included for the safety of you and your home.

Note: This article was written for a US audience, so I refer to the protective conductor as "ground". However, it is also called "earth" in other countries. Another difference is that the term "hot" is used, which is also known as "live". The third difference is that a split-phase 120/240 volt supply is provided to most homes in the US, resulting in a 240-volt supply between the two hots in addition to a 120-volt supply. This 240-volt supply is for powering higher powered appliances.

Re-Discovering the Mill Stream Arch

One mill is marked on the OSI c.1837 first-edition six-inch map. Image courtesy the National Library of Scotland, licence CC-BY.

I hadn't seen it since around 1982 or '83. I thought it was covered with scrub and brambles over the decades, but not so. This is a good time of the year to investigate it before the brambles get going. My theory is that it could have been the opening to a culvert/mill race that diverted water to a second mill in the adjoining field beside the cemetery car park or it may have been the return feed to the stream. One mill is marked on the 6-inch, first-edition OSI map and was located just over the wall from where the bins used to be kept in the cemetery. The ruin is still there. There's an arched culvert under the Mile Mill road, south of the lodge, that fed water to this mill.
I think the arched opening into the stream is unlikely to be a latrine outlet or drain as it's too wide. I thought most of the arch was submerged below the waterline, but possibly the bed of the stream has dropped over the last four decades due to erosion. Anyway, I didn't have a camera with me. That's a shame because the arch was nicely lit up by the setting sun.
Will investigate further tomorrow and take some photos.

The map above is a ChatGPT-sharpened version of a screenshot of the c. 1837 first-edition six-inch map available on the National Library of Scotland website. The scans appear to be a bit clearer than those available on Tailte Éireann's Irish Townland and Historical Map viewer.
Map reproduction licence CC-BY, courtesy the National Library of Scotland.

YouTube Requirements and Broadband Speed

Connection speed required for YouTube. Image from Google Help

Unless you have lots of people in your home feeding off  your Internet service and sharing the bandwidth, ultra-high-speed connection promotions such as "Gigabit broadband" are just marketing hype. The table above shows the recommended connection speeds from Google for streaming video from YouTube. Vodafone keeps trying to sell me such a service using a fibre-optic connection that replaces copper wires to the cabinet and which would increase my speed from 100 Mbps to 1 Gbps, but I'm stubbornly refusing as the current speed is perfectly adequate. A faster connection probably increases upload speed (which I think is normally about one tenth of download speed), but most people aren't in a hurry when uploading, unless they can't wait to backup thousands of photos or put their latest video online. Eventually I'll have to give in, because copper lines, which Vodafone rent from Eir, will ultimately be replaced. The process is slow, because there are legacy systems that still require them. 
I ring Vodafone every year, three months before my contract is due for renewal and negotiate a loyalty discount, getting a six-month discount. It's only €5 per month for 6 months, but better than nothing.

A Child Can Push Harder Than a Lawn Mower Blade

AI image generated by Google Gemini.

Did you know that a child can probably produce more torque using their arm, than a lawn mower engine can generate to turn the blade? Surprisingly, the figure for the torque of a 5 hp engine used on a mower is 7 to 10 foot-pounds (ft·lbf) in the imperial system or 11.5 to 13.6 newton-meters (Nm). Applied torque is simply force multiplied by distance, so 1 pound-force applied over a distance of 1 foot from a pivot is 1 foot-pound. In the metric system, the unit of torque is the newton-metre (Nm). A torque of 1 Nm is equivalent to one newton—the SI unit of force—applied over a distance of one metre. The speed of a lawn mower blade is more important than torque, and blades are driven directly by the crankshaft without reduction or overdrive gearing. Blades typically spin at the engine speed of around 3000 RPM, giving a blade tip speed of around 200 mph, or 90 metres per second.

As we saw in the article Interesting Facts - What is Torque?

power = torque x angular rotation speed

So while a child may be able to exert more torque with their arm than a mower engine can exert on a blade, they wouldn't be able to match its power. Another piece of the jigsaw is that the quoted figure of 11 to 13 Nm is for the drive torque from the engine. Since a blade is spinning at around 3000 RPM, it has a lot of inertia. The technical term for this when a rotating body such as a flywheel or blade is involved is moment of inertia. When a blade slows down as it impacts grass, the change in angular momentum creates a force, just like the way a car or any linearly-moving object creates a force as it slows down due to friction, or when it hits something (think of the huge force produced by a hammer, typically many tonnes, when it hits a nail). So the force produced by a blade as it impacts and shears grass is much greater than the force that the engine itself could have generated.

Note: You may be wondering why "newton" in "newton-metres" above isn't capitalised.  The unit is named after the English scientist Isaac Newton. It's not a typo. In the International System of Units (SI), or Système international d'unités, units named after a person are not capitalised. However, the symbol is, N in this case, Units are normally lower case, as are prefixes. However, prefixes over one million are capitalised—so kilometres is km, but gigahertz is GHz.

Cantilevered Boardwalks For Motorway Bridges?

Bridge over M9 Kilcullen Bypass on Sunnyhill Road. Image courtesy Google.

When Kildare County Council, or whoever was responsible, produced the spec for this bridge, (and the one over the M7 at the Bundle of Sticks Roundabout outside Naas), they left out foothpaths. Maybe it was lack of common sense and an attitude of "Sure, only cars go out there". Or perhaps it was due to penny pinching and lack of foresight and a narrow bridge was cheaper than one a couple of metres wider? Anyway, I'm wondering could boardwalks/cantilevered foothpaths be fixed onto the sides, exterior to the parapets?
It would obviously be impractical to install foothpaths on the inside of the parapets due to to both lanes being reduced in width. As it is, cars can't pass pedestrians safely without partially moving into the other lane. An article by Paul MacDonald, Kildare National Roads Office, on the construction of the M7 Newbridge Bypass and M9 Kilcullen Bypass is available on the Kilcullen Diary here.

The section about the earthing of the steelwork of the underbridge for the River Liffey is interesting—High voltage pylons can induce voltages and currents in conductors, potentially leading to different and hazardous potentials between isolated elements of a structure. Bonding them together eliminates these voltages and earthing a structure pulls the voltage down to ground (similar to the equipotential bonding in bathrooms, where metal objects such as drains, radiators, towel rails, water pipes and metal baths are bonded together):

Bridge over M9 Kilcullen Bypass on Sunnyhill Road. Image coiurtesy Google.

How to Calculate Bolt Circle Diameter (BCD) for Chainrings and Bash Guards

Bolt circle diameter (BCD). © Eugene Brennan

What Is a Bolt Circle Diameter (BCD) or Pitch Circle Diameter (PCD)?

As you may be aware, if you've found this guide, a bolt circle is an imaginary circle that passes through the centre of the bolt or screw holes in a round pattern. This is typically a wheel hub on a vehicle, chainring on a bicycle or flange on a pipe. The diameter of this circle is known as the bolt circle diameter (BCD) or pitch circle diameter (PCD).

Typically, BCD is quoted for chainrings on bikes and the bash guards that cover them, and you can calculate it by measuring the distance between the mounting holes of the chainring on the spider. If you need to order a part for a bicycle or check the BCD of a flange and can only measure the bolt hole spacing, you need to know the formula for working it out. Alternatively you can skip to the end of this guide where there are tables for various bolt spacings.

Thomas McGarry of McGarry's Lane

McGarry's Lane. © Eugene Brennan

I think I may have found the person who lent his name to the lane. 

The Primary Valuation, also known as Griffith's Valuation was a mid-19th property valuation in Ireland. Published between 1847 and 1864, it was the first full-scale survey of its kind, and collected information about the occupiers of land and buildings, their landlords and the amount and value of property held. Griffith's Valuation is searchable here on the Ask About Ireland Website.

In the valuation, a Thomas McGarry appears, with an address in Nicholastown. The Nicholastown townland extends out as far as Yellowbogcommon townland to the south and New Abbey townland to the east. I was aware of the presence of a building, visible on the first edition, c. 1837 6" Ordnance Survey map. This was located across the road from the cottage in McGarry's Lane. By the time the c. 1900 last-edition 25" OSI map was drafted, this building had disappeared. It appears from the map and record below that Thomas McGarry was listed as an occupier of the 8 acres and 3 roods of land on which the building stood, with Robert Brereton as lessor (The owner of New Abbey House). 

Valuation book showing the entry for Thomas McGarry. Image courtesy Ask About Ireland.

Map showing corresponding parcel of land leased by Thomas McGarry (16). Map attribution: Ask About Ireland.

The Tithe Applotment Books, however, show no record of a Thomas McGarry. These books were records of tithes, a form of religious tax paid to the established church in Ireland—the Anglican Church of Ireland. Tithes were extremely unpopular, as the Roman Catholic majority also had to pay them, leading to the Tithe War of the 1830s and eventual repeal of the tax by The Irish Church Act 1869, which disestablished the Church of Ireland. In the records, there are three entries for a John McGarry, and he's recorded as having paid 3/3½  (three shillings, three and a half pence) in one of these records. No information is available on whether John was a brother or father of Thomas. I found a death record for Thomas McGarry on the Irish Genealogy website. He died on 14th March, 1889, with the location indicated as "New Abbey".
It's possible he's buried in New Abbey Cemetery.

Tithe payment by a John McGarry. Image attribution: The National Library of Ireland

The Tithe Applotment database search page is available here.  Image attribution: National library of Ireland

Death record for Thomas McGarry. Image attribution: Irish Genealogy.

The structure shown on the map was located behind this fence. No trace remains.  © Eugene Brennan