numbering-systems.md

Numbering Systems

Decimal (base 10) — uses numbers 0-9

102	101	100
1	2	8

Calculation	Result
8 x 100	8
2 x 101	20 (2x10)
1 x 102	100 (1x10x10)
Total	128

Binary (base 2) — uses numbers 0 and 1

23	22	21	20
1	0	0	1

Calculation	Result
1 x 20	1
0 x 21	0
0 x 22	0
1 x 23	8 (1x2x2x2)
Total	9

1001 binary = 9 decimal

Hexadecimal (base 16) — uses numbers 0-9 and letters A-F

162	161	160
2	3	F

Calculation	Result
F x 160	15
3 x 161	48 (3x16)
2 x 162	512 (2x16x16)
Total	575

23F hexadecimal = 575 decimal

Binary, Decimal, Hexadecimal Conversion

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