 # Binary and hexadecimal conversions

Updated: 05/21/2018 by Computer Hope

## Binary Computers work on the principle of number manipulation. Inside the computer, the numbers are represented in bits and bytes. For example, the number three is represented by a byte with bits 0 and 1 set to "00000011" which is a numbering system using base 2. People commonly use a decimal or Base 10 numbering system.

What this means is that, in Base 10, you count from 0 to 9 before adding another digit. For example, the number 22 in Base 10 means we have two sets of 10's and two sets of 1's.

Base 2 is also known as binary since there can only be two values for a specific digit; either a 0 = OFF or a 1 = ON. You cannot have a number represented as 22 in binary notation. The decimal number 22 is represented in binary as 00010110. By following the below chart, that breaks down to:

Bit Position 7 6 5 4 3 2 1 0
1 1 1 1 1 1 1 1
Decimal 128 64 32 16 8 4 2 1

22 or 00010110:

All numbers representing 0 are not counted, 128, 64, 32, 8, 1 because 0 represents OFF.

However, numbers representing 1 are counted, 16 + 4 + 2 = 22 because 1 represents ON.

Decimal Binary
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
16 10000
32 100000
64 1000000
100 1100100
256 100000000
512 1000000000
1000 1111101000
1024 10000000000

## Hexadecimal

Another numbering system used by computers is hexadecimal, or Base 16. In this system, the numbers are counted from 0 to 9, then letters A to F, before adding another digit. The letters A through F represent decimal numbers 10 through 15, respectively. The below chart indicates the values of the hexadecimal position compared to 16 raised to a power and decimal values. It is much easier to work with large numbers using hexadecimal values than decimal.

To convert a value from hexadecimal to binary, you merely translate each hexadecimal digit into its 4-bit binary equivalent. Hexadecimal numbers have either a 0x prefix or an h suffix.

For example, consider the hexadecimal number:

`0x3F7A`

Using the Binary chart and the Hex chart below, this translates into the binary value:

`0011 1111 0111 1010`
Decimal Hexadecimal Binary
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111

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