Binary and Decimal

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Binary and Decimal defenitions

Binary is a counting system similar to the one that you use normally. Each place represents a new value and it is expressed with digits. The difference is that Binary is Base 2 which means that there can only be 2 symbols, 1 and 0. Each place in Binary is double that of the one to the right (so the first is 1, the one to the left is 2, then 4 and so on). If there is a 1 in a place (or bit) then it is counted when calculating the number. Often binary is used in computing as it can express large quantities of numbers using only 0's and 1's, which can be physically represented with on and off with a light. In computing a computer will often only use 1 Byte (8 bits) per program part and so can only count from 0 to 255. Despite this Binary, like any counting system, can count to any number. Various examples include:


1 - 1 (1 is on)

10 - 1010 (8 and 2 are on, 8+2=10)

56 - 111000 (32, 16 and 8 are on, 32+16+8=56)


Decimal (or Denary) is base 10, the counting system that you're used to. There are 10 different symbols, 0-9, and each place to the left is 10 times that of the right. Some examples include:

1 - 1

10 - 10

56 - 56

124257390475903122905 - 124257390475903122905

Binary vs Decimal Mathematics

Examples of conversions in Binary and Decimal:


Binary to Decimal:

1001001: 73

100: 4

11111111: 255

Decimal to Binary:

64: 1000000

79: 1001111

139: 10001011