Eugene is a qualified control/instrumentation engineer Bsc (Eng) and has actually functioned as a developer of electronic devices & software program for SCADA systems.

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The Binary System

The binary numbering device is the basis for storage, transfer and also manipulation of information in computer system devices and digital electronic devices. This system uses base 2 quite than base 10, which is what we are acquainted with for counting in everyday life. By the finish of this easy-to-understand also write-up, you'll have a master of why binary is provided in computer systems and electronics.

What Is Decimal and Why Do We Use It?

The decimal, base 10 or denary numbering mechanism is what we are acquainted via in day-to-day life. It uses 10 icons or numerals. So you count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . . . yet there is no character for the next number, the integer value we interpret as "ten". Ten is therefore represented by 2 digits: the character 1 adhered to by 0 or "10", which really means "one ten and also no units". Similarly, one hundred is represented by 3 digits: 1, 0 and 0; i.e., one hundred, no 10s and also no units".

Basically numbers are represented by a collection of numerals in the devices, 10s, hundreds, thousands area and so on For circumstances, 134 means one hundred, 3 tens and also 4 systems. The decimal device probably arose because we have 10 fingers on our hands, which might be supplied for counting.

What Is Binary and How Does It Work?

The binary mechanism used by computer systems is based upon 2 numerals: 0 and also 1. So you count 0, 1, but tright here is no character for 2. So 2 is stood for by 10 or "one 2 and no units". In the very same way that tright here is a systems, tens, hundreds, thousands area in the decimal mechanism, in the binary system tright here is a devices, twos, fours, eights, sixteenagers place and so on in the binary system. So the binary and also decimal equivalents are as below:

00000000 = 000000001 = 100000010 = 200000011 = 300000100 = 400000101 = 500000110 = 600000111 = 7 (and so on)

Counting in Binary and Decimal



A published circuit board (PCB) through digital included circuits (ICs or "chips")

Olafimages, public domain photo via

Why Do Computers Use Binary?

"A single switch can be on or off, enabling the storage of 1 bit of indevelopment. Switches can be grouped together to keep bigger numbers. This is the key reason why binary is supplied in digital systems."

How Is Binary Used in Digital Computers and also Electronic Devices?

Numbers can be encoded in binary format and stored utilizing switches. The digital innovation which provides this mechanism could be a computer system, 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 picture below. Each switch could represent 1 or 0 relying on whether it is turned on or off. So you think of a number and collection the switches on or off to "store" the binary value of this number. If someone else then looked at the switches, they can "read" the number. In a computer, switches are enforced utilizing transistors. The smallest memory configuration is the bit, which have the right to be imposed with one switch. If 8 switches are added together you gain a byte. The digital hardware is able to collection the switches on and also off (i.e. compose data) and also likewise check out the state of the switches. In the conceptual picture below, tright here are 8 switches and 2 to the power of 8 = 256 permutations or arrangements relying on whether a switch is on or off. If on represents 1 and off represents 0, the group of switches can reexisting any of the following worths.

00000000 0 decimal00000001 1 decimal00000010 2 decimal00000011 3 decimal00000100 4 decimal...11111110 254 decimal11111111 255 decimal

In an digital tool or computer, bereason of micro-miniaturization, billions of switches deserve to be incorporated onto integrated circuits (IC), possibly allowing the storage and manipulation of astronomical quantities of indevelopment.


Conceptual concept of just how the state of a bank of eight switches permits the "storage" of 2 to the power of 8 = 256 possible numbers

© Eugene Brennan






































Representing Non-Integer Values in Computer Systems

Integers can be stored and processed straight as their binary equivalents in computer systems; however, this isn't the instance through various other information. A machine such as a computer, digital camera, scanner etc cannot directly store decimals, non-numerical (message, photo, video) or analog measurement data from the real civilization straight. This kind of data could be:

Person's name or addressTemperature measured in a roomImage from a digital video camera or scanner.AudioVideoDecimal number

Representing Documents in Floating Point Format

Decimal numbers are represented in computer devices using a mechanism recognized as floating allude. A decimal number have the right to be stood for about, to a particular level of accuracy by an integer significand also multiplied by a base, elevated to the power of an integer exponent.

Processing and Storage of Analog Data

A voltage level from a temperature sensor is an analog signal and also has to be converted to a binary number by an equipment referred to as an analog to digital converter (ADC). These devices have the right to have actually assorted reoptions and for a 16 little bit converter, the signal level is stood for by a number from 0 to 216 = 65535. ADCs are additionally offered in photo scanners, digital camages, and in digital devices supplied to record sound and video to transform the real human being analog signals into data that deserve to be stored in memory. Imperiods created in a drawing package are additionally stored as individual pixels and a byte of information is used for the red, green and blue intensity levels of each pixel.What's the Difference Between Analog and Digital? explains this in more detail.


Digital signals in electronic circuiattempt are either high or low, representing a "1" or "0"

© Eugene Brennan

Encoding Text File as ASCII

Names, addresses or various other text entered into a computer can't be stored straight in computer system memory. Instead the message is broken dvery own right into individual letters, numerals and various other non alphanumeric characters (e,g, &*£$# etc) and a coding mechanism referred to as ASCII represents each character by a number from 0 to 127. This information is then stored in binary format as one or even more bytes in memory, each byte being made up of individual bits, and each little imposed utilizing transistors.

ASCII Table Hex, Binary and also Decimal Values

Table showing ASCII personalities via their hexadecimal, binary and also decimal values. Hexadecimal or "hex" is a convenient method of representing a byte or word of data. Two personalities can reexisting 1 byte of information.

ASCII code table. ASCII assigns a number from 0 to 127 to letters, numbers, non alphanumeric personalities and also regulate codes

Public domain image through Wikimedia Commons

What Is Machine Code and also Assembly Language?

Not only are values or data stored in memory, however likewise the instructions which tell the microprocessor what to perform. These instructions are referred to as machine code. When a software program regimen is written in a high level language such as BASIC, Java or "C", another routine dubbed a compiler breaks the program down into a collection of standard instructions called machine code. Each machine code number has actually a unique function which is taken by the microprocessor. At this low level, instructions are standard arithmetic features such as add, subtract and multiply entailing the contents of memory locations and registers (a cell which deserve to have arithmetic operations brought out on it). A programmer deserve to additionally compose code in assembly language. This is a low level language comprising instructions known as mnemonics which are supplied to move information in between registers and memory and also perdevelop arithmetic operations.

How to Convert Decimal to Binary and also Binary to Decimal

You deserve to convert decimal to binary using the remainder technique. See my overview for details:

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 math which encounters variables which can only have among two claims, true or false. In the 1930s Boole's work was uncovered by the mathematician and also engineer Claude Shannon, who realized it can be provided to simplify the architecture of telephone switching circuits. These circuits originally provided relays which might be either on or off, and the preferred output state of the device, depending upon the combination of states of the inputs, might be explained by a Boolean algebraic expression. Boolean algebra rules can then be offered to simplify the expression, causing a reduction of the number of relays compelled to implement a switching circuit. At some point Boolean algebra was applied to the architecture of digital electronic circuiattempt as we will certainly view below.

Digital Logic Gates: AND, OR and NOT

A digital state, ie high/low or 1/0 deserve to be stored in a one-little bit cell in memory, however what if that information hregarding be processed? The many fundamental handling element in a digital digital circuit or computer is a gate. A gate takes one or even more digital signals and generates an output. Tbelow are three forms of gates: AND, OR and NOT (INVERT). In their easiest develop, little teams of gates are obtainable on a single IC. However, a complex combinationwide logical attribute can be imposed utilizing a Programmable Logic Array (PLA) and even more advanced devices such as microprocessors are written of numerous entrances and memory storage cells.

For an AND gate, the output is true or high only as soon as 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 deserve to be used to expush what the output signal of a circuit have to be, depending on the combination of inputs. The major operations in Boolean algebra are and, or and not. Throughout a design procedure, the compelled value of an output for all the various permutations of input claims can be tabulated in a truth table. The worth '1' in the fact table indicates an input/output is true or high. The worth '0' indicates the input/output is false or low. Once a reality table is developed, a Boolean expression can be composed for the output, streamlined and also applied using a repertoire of logic gates.

So a typical Boolean expression via 3 independent variables A, B and C and also one dependent variable D would certainly be:

Y = A.B + C

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

This content is precise and also true to the ideal of the author’s understanding and also is not supposed to substitute for formal and also individualized advice from a qualified professional.

Questions & Answers

Question: What voltperiods are offered for 1 and also 0 in a digital circuit?

Answer: It depends on the modern technology. Sometimes a voltage cshed to zero is supplied for logic 0 and a higher voltage is provided for logic 1. However in the instance of some serial data transmission standards, a negative voltage represents logic 1 and also a positive voltage represents logic 0. Several voltage levels are used by digital incorporated circuits (chips), e.g. 5 v logic supplies volteras reduced than this for logic 1 and 3 volt logic offers even lower voltperiods. RS232 information transmission might use volteras cshed to +1 20 volts.

Question: Why can't we use -1 in digital electronics?

Answer: -1 or various other negative numbers are commonly implemented making use of two's enhance. So to represent -1 in two's match form, invert the bits and add 1:

So 1 is 001

Inverting the bits gives


Adding 1 gives


Remember this is simply a conventional means of representing an adverse number in a digital device so that arithmetic can be done and job-related out ok.

or in binary 111 + 001 = 1000.

Due to the fact that just three bits are used, the fourth little would certainly be "unseen" by the digital device and also the result in this example would be understood as 000 or zero.

You can even more around two's compliment here:

Question: Which characteristic of a transistor is useful for digital counting and manipulation, and why?

Answer: A transistor can behave as a regulated switch and form component of an elementary circuit element dubbed a flip-flop. A flip-flop have the right to store one little of information, and in enhancement to various other circuit aspects, a greater level device called a binary respond to deserve to be enforced.

Question: What are the applications of a binary encoding system?

Answer: Binary encoding is a system of transmitting binary data over a connect designed to handle message data. e.g. email.

You have the right to review more about it here:

Question: What is 16 in the octal number system?

Answer: If you intend 16 is an octal number, and also you want to convert to decimal, the answer is 16 = 1 x 8 + 6 = 14 decimal.

If you mean how execute I represent 16 decimal in the octal numbering device (base 8), the answer is 20 (2 in the "eights" place).

Question: What are high and also low in a digital circuit?

Answer: "1" and also "0" by convention reexisting "high" and "low" in a digital circuit.

© 2012 Eugene Brennan


Nima on June 15, 2018:

The write-up was really valuable for my research studies.. You did it exceptionally well . Thank you incredibly a lot for the information

Eugene Brennan (author) from Ireland on April 15, 2018:

Hi Chirayu,

In the time before advanced computer system graphics and as soon as displays might just show text, alphanumeric personalities were presented on display using a chip referred to as a character generator ROM (Read Only Memory). This converted ASCII bytes in memory into a rectangular matrix of dots representing the character that circuitry in the computer and monitor might display screen.

Here's some details on exactly how Atari computers offered to job-related.

Nowadays every little thing you see on display is stored as a raster image in memory with 3 bytes for each pixel you see on display screen. One byte is for red, one for blue and also one for green. Depending on the worth of the 3 bytes, you can gain 16 million various shades of colours.

Have a look at this tutorial which gives even more information.

Chirayu on April 15, 2018:

Hello sir

I have actually a question ....

How computer system imagine the design and form of the binary code which we are composing ....

For example :- I ideal eight in binary of so how computer imagine and also style the shape of eight on the screen

Kefas on January 03, 2018:

Great write-up, save up with the brilliant work.

Kiran on July 11, 2017:

U males made my problem simple now I m topper in electronic devices first I acquired 60% now I am acquiring 99%

Robert Sacchi on March 20, 2017:

It is a very great article that explains things very well. There is a easier albiet less polished unsleek technique of convariation. Decimal 27 to binary:

32 16 8 4 2 1

0 1 1 0 1 1 = 16+8+2+1 = 27

Binary 1011010 to decimal:

64 32 16 8 4 2 1

1 0 1 1 0 1 0 = 64+16+8+2 = 90 Decimal

5A Hexidecimal = 132 Octal

Crude yet effective.

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Dan Harmon from Boise, Idaho on August 05, 2012:

You explained this extremely well. Many kind of years back I experimented on programming in machine language - what a hassle! It didn't take long to relocate to somepoint higher.