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

Further Reading