Binary, decimal, and hexadecimal conversions
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:
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 values and binary equivalents chart
Another numbering system used by computers is hexadecimal (hex), 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's easier to work with large numbers using hexadecimal values than decimal.
To convert a value from hexadecimal to binary, you 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:
Using the Binary chart and the Hex chart below, this translates into the binary value:
0011 1111 0111 1010