Notes on understanding binary, decimal, hexadecimal numbers and conversions.

Learning Objectives

Convert from binary to decimal and vice versa

Convert from binary to hexadecimal and vice versa

Convert from hexadecimal to decimal and vice versa

Decimals or Base 10

Decimal system uses 10 as a base and the numbers range from 0 to 9.

129 = 100 + 20 + 9
9 = 9 * 10^0 (Note that 10^0 is equal to 1)
20 = 2 * 10^1
100 = 1 * 10^2
Powers of ten
10^0 = 1
10^1 = 10
10^2 = 100
10^3 = 1000

Binary or Base 2

Binary numbers are base 2 numbers and have only two values: 0 and 1.

Binary 101 has 1 in the units column, 0 in the 2s column and 1 in the 4s column.
1 = 1 * 2^0 units
0 = 0 * 2^1 twos
1 = 1 * 2^2 fours
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8