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What is Binary?

By Brendan McGuigan
Updated May 16, 2024
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Binary is a numeric system which uses two numerals to represent all real numbers. While the most common counting system, the decimal system, uses ten numerals, binary uses only 0 and 1.

Each digit in a binary number system therefore represents a power of two. The first digit on the right represents the 0th power, the second represents the 1st power, the third represents the 2nd power, and so on. So the number 1 in the decimal system is represented also as 1 in the binary system. The number 23, by contrast, is represented as 10111 (16+0+4+2+1).

The decimal system makes perfect sense for human beings to use. We have ten fingers and ten toes, so when early humans began counting things they turned to these readily available markers. Later, when systems of counting became codified, it was natural to convert the already used decimal system to a representational system. Binary is also a fairly natural system, however, since many things either "are" or "are not." Many spiritualist traditions, such as the Pythagoreans and some Indian mystics, therefore made use of this system, beginning in the 6th century BC.

In 1854, a central paper on binary systems was published by the mathematician George Boole. This paper laid out the groundwork for what would eventually be called Boolean algebra. With the advent of electronics, these systems suddenly made incredible sense. Most electronic systems function on a switch-based system, with current either running or not running. In 1937, Claude Shannon set out the foundations for the theory of circuit design using binary arithmetic. In 1940, the age of binary computing began with the release of Bell Labs Complex Number Computer, which was able to perform extremely complex mathematical calculations using this type of system.

In a more general sense, binary systems can be anything which offers only two options, not necessarily limited to numerical systems. In the case of electronic switches, for example, the system consists of current-no current. A true-false exam is another example. Yes-no questions are also binary in nature.

Mathematical methods exist for transforming binary numbers into decimal numbers, and visa-versa. There are also mathematical devices for performing functions such as addition, subtraction, multiplication and division in different base-systems, including binary. While conversion to or from decimal is somewhat labored, converting between binary and octal or hexadecimal systems, base-eight and base-16 respectively, is much easier. This is because both eight and 16 are powers of two, making them integrate well with binary systems. It is for this reason that both octal and hexadecimal are widely used base-systems in computer applications.

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Discussion Comments
By anon357630 — On Dec 05, 2013

Whoever invented this system was really clever!

By anon305401 — On Nov 26, 2012

101010100000 -- like that?

By anon297037 — On Oct 14, 2012

This is fascinating! My brother keeps talking about this, asking if I've learned it yet, and because I love him I looked it up. He'll be surprised!

By anon163598 — On Mar 28, 2011

could you please include when you posted this article-month, day, year? It'll help for citing purposes. Thanks!

By anon114035 — On Sep 27, 2010

Binary Code is most commonly used in BIOS(Basic Input Output System).Which is used in computers

Binary numbers (1 or 0) represent on(1) or off(0).

Typically you work out binary like this:

256 128 64 32 16 8 4 2 1

If you have say a decimal number of 254, to work out the binary code you would use the system above to work it out. So,

256 128 64 32 16 8 4 2 1

0 1 1 1 1 1 1 1 0

The number that was given (254) is equated in the system above if you were to add up the numbers that have 1s underneath them.From there you can learn to translate binary into decimal, decimal into hexidecimal (not using binary,because hex is a whole other language base) which then goes onto C++ programming and all the rest.

If you're working out bigger numbers, for instance 3813, then you need to create a bigger system in order to work out the binary code so therefore you need to do this:

2048 1024 512 256 128 64 32 16 8 4 2 1

1 1 1 0 1 1 1 0 0 1 0 1

So this is your Binary Code for 3813:

1 1 1 0 1 1 1 0 0 1 0 1

If you want to be lazy you can just use your calculator on your computer. You need to switch the view to scientific which calculates binary, decimal, hex and octal. I suggest you make sure you understand binary code first before moving onto hex because the development between them can become very confusing.

I hope this makes sense.

By anon90397 — On Jun 15, 2010

A "Binary Number" is a number from a base-2 counting system.

Humans count in base-10.

Several of the posts show how to convert binary numbers (up to eight columns in length) to a base-10 number.

To count in binary means you only have two numbers, 0 and 1!

Starting from zero and counting up to seven would look like this: 0, 1, 10, 11, 100, 101, 110, 111.

This allows you to keep track of eight things, don't forget about zero.

By anon67339 — On Feb 24, 2010

from left to right

first zero = 128

second zero = 64

third zero = 32

fourth zero = 16

fifth zero = 8

sixth zero = 4

seventh zero = 2

eighth zero = 1

00000001 - 1

WHY?

(128*0)+(64*0)+(34*0)+(16*0)+(8*0)+(4*0)+(2*0)+(1*1) = 1

00000010 - 2

00000011 - 3

00000100 - 4

00000101 - 5

...

00010100 = 20

(128*0)+(64*0)+(32*0)+(16*1)+(8*0)+(4*1)+(2*0)+(1*0)= 0+0+0+16+0+4+0+0 = 20

sorry if there are any typos. i did it quickly.

By anon65105 — On Feb 11, 2010

binary: 10100 = 20?

solution:

256 128 64 32 16 8 4 2 1

0 0 0 0 1 0 1 0 0

so;

16+4 = 20

By anon49445 — On Oct 20, 2009

think of it in columns, just like the numbers you use every day. the number - 1,234 right? the four represents 4 of ones. the three represents 3 of tens. the two represents 2 of one hundreds. the one represents 1 of one thousand. you understand that the number 1,000 is actually just a representation of one thousand of a single number 1. binary is the same, but with different columns. instead of ones, tens, hundres, thousands, hundred-thousands, millions... you have ones, twos, fours, eights, sixy fours, etc. get it?

By anon49293 — On Oct 19, 2009

This wasn't very useful at all. it just sounds like abunch of numbers representing other numbers.

By anon43875 — On Sep 02, 2009

@8 Yes, that is correct. the far right column denotes you 2^0 which, if there is a 1 there, 2^0 equals 1, the second place is 2^1 which, following this pattern equals 2

so from 1 to 10: 1; 10; 11; 100; 101; 110; 111; 1000; 1001; 1010.

By anon43411 — On Aug 28, 2009

So, let me get this straight (Hopefully)

10100 = 20? If not. Why not?

By anon42335 — On Aug 20, 2009

I still do not understand this code. O.o

By Jahpanah — On Feb 17, 2009

Hi According to your query a binary means on or off state for any data used digital world.

By anon17819 — On Sep 08, 2008

Well - After all the work I completed... it seems that absolutely no one wants the truth... So, I ask all of you, which includes the Editorial Staff:

'What is the definition of a Binary Number?'

Because I concluded that the definition of a Binary Number, must be defined as;

A Binary Number is the Exponent in a Base 2 Exponential Operation.

By rjohnson — On Feb 10, 2008

Typically in binary systems that need to indicate something is either yes/no or true/false, 0 is used for "no" or "false," and 1 is used for "yes" or "true."

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