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

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The Binary System

The binary numbering system is the basis because that storage, transfer and manipulation that data in computer system systems and digital digital devices. This system uses basic 2 fairly than basic 10, i beg your pardon is what us are familiar with because that counting in day-to-day life. Through the finish of this easy-to-understand article, you'll have a understand of why binary is supplied in computers and also electronics.

What Is Decimal and Why carry out We usage It?

The decimal, base 10 or denary numbering mechanism is what we are familiar with in day-to-day life. It uses 10 icons or numerals. For this reason you count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . . . Yet there is no numeral for the next number, the integer worth we interpret as "ten". Ten is as such represented by two digits: the numeral 1 followed by 0 or "10", i m sorry really means "one ten and no units". Similarly, one hundred is stood for by three digits: 1, 0 and 0; i.e., one hundred, no tens and no units".

Basically number are stood for by a collection of number in the units, tens, hundreds, thousands ar etc. Because that instance, 134 method one hundred, 3 tens and also four units. The decimal device probably developed because we have actually 10 fingers on our hands, which can be used for counting.

What Is Binary and also How Does the Work?

The binary device used by computer systems is based on two numerals: 0 and 1. So you counting 0, 1, yet there is no numeral for 2. Therefore 2 is stood for by 10 or "one 2 and no units". In the same way that over there is a units, tens, hundreds, thousands location in the decimal system, in the binary system there is a units, twos, fours, eights, sixteens location etc. In the binary system. For this reason the binary and decimal equivalents space as below:

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

Counting in Binary and also Decimal



A printed circuit plank (PCB) with digital integrated circuits (ICs or "chips")

Olafpictures, publicly domain image via

Why Do computer systems Use Binary?

"A solitary switch can be top top or off, allowing the warehouse of 1 bit of information. Switches deserve to be grouped with each other to store bigger numbers. This is the an essential reason why binary is used in digital systems."

How Is Binary offered in Digital Computers and Electronic Devices?

Numbers have the right to be encoded in binary format and stored using switches. The digital modern technology which offers this system could be a computer, calculator, digital TV decoder box, cell phone, housebreaker alarm, clock etc. Values are stored in binary style in memory, which is basically a bunch of electronic on/off switches.

Imagine if you had actually a financial institution of 8 rocker switches just like in the photo below. Each switch might represent 1 or 0 depending upon whether that is rotate on or off. So girlfriend think the a number and set the switches top top or off to "store" the binary value of this number. If who else then looked at the switches, they might "read" the number. In a computer, switches are applied using transistors. The the smallest memory construction is the bit, which have the right to be implemented with one switch. If 8 switches are added together you obtain a byte. The digital hardware is may be to set the switches on and also off (i.e. Write data) and also read the state the the switches. In the theoretical image below, there room 8 switches and 2 to the strength of 8 = 256 permutations or arrangements depending on whether a move is top top or off. If on to represent 1 and off represents 0, the team of switches have the right to represent any kind of of the following values.

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

In one electronic machine or computer, due to the fact that of micro-miniaturization, billions the switches can be included onto incorporated circuits (IC), potentially enabling the storage and manipulation of huge amounts that information.


Conceptual idea of exactly how the state of a bank of eight switches enables the "storage" the 2 come the power of 8 = 256 feasible numbers

© Eugene Brennan






































Representing Non-Integer worths in computer system Systems

Integers have the right to be stored and also processed straight as your binary equivalents in computer system systems; however, this isn't the case with other data. A machine such as a computer, digital camera, scanner and so on cannot straight store decimals, non-numerical (text, image, video) or analog measurement data indigenous the real human being directly. This type of data could be:

Person's name or addressTemperature measure in a roomImage indigenous a digital camera or scanner.AudioVideoDecimal number

Representing Data in Floating point Format

Decimal numbers are stood for in computer system systems making use of a system well-known as floating point. A decimal number have the right to be stood for approximately, come a particular level the accuracy by an integer significand multiply by a base, raised to the power of an essence exponent.

Processing and Storage of Analog Data

A voltage level indigenous a temperature sensor is one analog signal and also has to be convert to a binary number by a device called an analog come digital converter (ADC). These gadgets can have various resolutions and also for a 16 little bit converter, the signal level is stood for by a number indigenous 0 come 216 = 65535. ADCs are likewise used in image scanners, digital cameras, and also in electronic equipment offered to record sound and video clip to transform the real world analog signals right into data that can be save on computer in memory. Images created in a drawing package are likewise stored as individual pixels and a byte the data is supplied for the red, green and also blue intensity level of each pixel.What's the Difference in between Analog and also Digital? describes this in an ext detail.


Digital signal in electronic circuitry space either high or low, representing a "1" or "0"

© Eugene Brennan

Encoding text Data as ASCII

Names, addresses or various other text gone into into a computer can't be stored straight in computer memory. Rather the message is broken down right into individual letters, numerals and also other non alphanumeric characters (e,g, &*£$# etc) and also a coding system dubbed ASCII represents each character through a number native 0 to 127. This data is then stored in binary style as one or an ext bytes in memory, each byte being consisted of of individual bits, and also each bit implemented using transistors.

ASCII Table Hex, Binary and Decimal Values

Table reflecting ASCII personalities with your hexadecimal, binary and decimal values. Hexadecimal or "hex" is a convenient means of representing a byte or native of data. Two characters can stand for 1 byte of data.

ASCII code table. ASCII assigns a number from 0 to 127 to letters, numbers, no alphanumeric characters and also control codes

Public domain picture via Wikimedia Commons

What Is an equipment Code and also Assembly Language?

Not only are values or data save in memory, but additionally the instructions which phone call the microprocessor what come do. This instructions are called device code. Once a software regime is written in a high level language such as BASIC, Java or "C", one more program dubbed a compiler breaks the routine down right into a collection of basic instructions called device code. Each maker code number has actually a unique function which is understood by the microprocessor. In ~ this short level, accuse are simple arithmetic attributes such together add, subtract and multiply including the materials of storage locations and registers (a cabinet which have the right to have arithmetic operations brought out on it). A programmer can likewise write code in assembly language. This is a low level language comprising instructions well-known as mnemonics which are offered to relocate data between registers and also memory and also perform arithmetic operations.

How to convert Decimal to Binary and also Binary to Decimal

You can convert decimal to binary making use of the remainder method. Check out my overview for details:

How to convert Decimal come Binary and Binary come Decimal

George Boole and also Boolean Algebra

Boolean algebra, emerged by the british mathematician George Boole in the 19th century, is a branch of math which deals with variables which can only have one of 2 states, true or false. In the 1930s Boole's work-related was uncovered by the mathematician and engineer Claude Shannon, who realized it might be provided to simplify the style of telephone convert circuits. These circuits originally provided relays which can be either on or off, and the wanted output state that the system, depending upon the combination of says of the inputs, could be explained by a Boolean algebraic expression. Boolean algebra rules might then be offered to simplify the expression, causing a reduction of the variety of relays forced to implement a switching circuit. Ultimately Boolean algebra was used to the design of digital digital circuitry as we will see below.

Digital reasonable Gates: AND, OR and NOT

A digital state, in other words high/low or 1/0 have the right to be save on computer in a one-bit cell in memory, but what if the data has to be processed? The most simple processing aspect in a digital digital circuit or computer system is a gate. A door takes one or much more digital signals and also generates an output. There room three species of gates: AND, OR and also NOT (INVERT). In their most basic form, little groups of gateways are available on a solitary IC. However, a complex combinational logical duty can be enforced using a Programmable Logic variety (PLA) and more sophisticated tools such as microprocessors are composed of countless gates and also memory storage cells.

For an and also gate, the output is true or high only as soon as both inputs room true.For one OR gate, the output is high if either or both inputs space true.For a no gate or inverter, the calculation is the opposite state come the input.

Boolean algebraic expressions deserve to be offered to express what the output signal the a circuit need to be, depending on the mix of inputs. The key operations in Boolean algebra space and, or and also not. During a architecture process, the compelled value of an output for all the assorted permutations of intake states can be tabulated in a truth table. The value '1' in the reality table means an input/output is true or high. The worth '0' way the input/output is false or low. Once a reality table is created, a Boolean expression can be composed for the output, simplified and also implemented using a repertoire of reasonable gates.

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

Y = A.B + C

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

This content is accurate and also true come the finest of the author’s knowledge and also is not intended to substitute for formal and individualized advice indigenous a default professional.

Questions & Answers

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

Answer: It counts on the technology. Occasionally a voltage close come zero is used for reasonable 0 and also a greater voltage is used for logic 1. Yet in the situation of part serial data infection standards, a an unfavorable voltage represents logic 1 and also a positive voltage represents logic 0. Numerous voltage levels are supplied by digital combined circuits (chips), e.g. 5 v logic uses voltages reduced than this for logic 1 and also 3 volt logic uses also lower voltages. RS232 data transmission might use voltages close to +1 20 volts.

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

Answer: -1 or other an unfavorable numbers room normally implemented using two's complement. Therefore to represent -1 in two's enhance form, invert the bits and include 1:

So 1 is 001

Inverting the bits gives


Adding 1 gives


Remember this is simply a conventional method of representing a an unfavorable number in a digital mechanism so the arithmetic have the right to be done and also work out ok.

or in binary 111 + 001 = 1000.

Because only three bits are used, the fourth bit would certainly be "unseen" through the digital system and also the result in this example would be interpreted as 000 or zero.

You can much more about two's compliment here:

Question: i beg your pardon characteristic of a transistor is advantageous for digital counting and manipulation, and also why?

Answer: A transistor can behave as a regulated switch and form part that an elementary circuit aspect called a flip-flop. A flip-flop can store one little of information, and also in enhancement to various other circuit elements, a greater level an equipment called a binary respond to can be implemented.

Question: What space the applications the a binary encoding system?

Answer: Binary encoding is a mechanism of transmitting binary data over a connect designed to take care of text data. E.g. Email.

You have the right to read an ext about it here:

Question: What is 16 in the octal number system?

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

If friend mean how do I stand for 16 decimal in the octal numbering device (base 8), the prize is 20 (2 in the "eights" place).

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

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

© 2012 Eugene Brennan


Nima ~ above June 15, 2018:

The post was really advantageous for my studies.. Girlfriend did it an extremely well . Give thanks to you very much for the information

Eugene Brennan (author) indigenous Ireland ~ above April 15, 2018:

Hi Chirayu,

In the moment before sophisticated computer graphics and when displays might only present text, alphanumeric characters were presented on display screen using a chip referred to as a personality generator ROM (Read just Memory). This convert ASCII bytes in memory into a rectangular matrix that dots representing the character that circuitry in the computer and also monitor can display.

Here's some information on how Atari computer systems used to work.

Nowadays whatever you check out on display screen is stored as a raster image in memory with 3 bytes because that each pixel you watch on screen. One byte is because that red, one for blue and also one because that green. Depending upon the worth of the 3 bytes, friend can gain 16 million various shades the colours.

Have a look in ~ this tutorial which gives more detail.

Chirayu ~ above April 15, 2018:

Hello sir

I have actually a concern ....

How computer imagine the design and also shape the the binary code which we space writing ....

For example :- I best eight in binary of for this reason how computer system imagine and design the form of eight top top the screen

Kefas on January 03, 2018:

Great article, save up through the brilliant work.

Kiran ~ above July 11, 2017:

U males made my difficulty easy currently I m topper in electronics first I got 60% now I am acquiring 99%

Robert Sacchi on in march 20, 2017:

It is a very good article that defines things an extremely well. Over there is a easier albiet less refined unrefined an approach of conversion. Decimal 27 come 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 but effective.

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Dan Harmon native Boise, Idaho on august 05, 2012:

You explained this an extremely well. Countless years back I experimented ~ above programming in machine language - what a hassle! it didn't take long to move to other higher.