Numeral Systems — Binary, Octal, Decimal, Hex, Base 36

Positional number systems write the same value with different bases. This page explains place value, the digits and prefixes used for each common base, and lists 0 to 32 in binary, octal, decimal, hex and base 36.

Place value in any base

In base b, each digit is multiplied by a power of b according to its position: the value of dₙ…d₁d₀ is dₙ·bⁿ + … + d₁·b + d₀. For example, binary 1011 = 1·8 + 0·4 + 1·2 + 1·1 = 11, and hex 2F = 2·16 + 15 = 47.

One hex digit is exactly four bits and one octal digit exactly three bits, which is why programmers use hex and octal as a compact way to write binary.

Common bases with their digits, programming prefixes and uses
Base	Name	Digits	Prefix	Typical use
2	Binary	0 1	0b	bits, logic, machine data
8	Octal	0–7	0o (older: leading 0)	Unix file permissions
10	Decimal	0–9	none	everyday numbers
16	Hexadecimal	0–9, A–F	0x	bytes, memory addresses, colors
36	Base 36	0–9, A–Z	none	short alphanumeric IDs

Sources: Ecma TC39: ECMAScript Language Specification (Number.prototype.toString radix 2–36)

Conversion table, 0 to 32

Every row below is computed by converting the decimal value to each base.

Numbers 0 to 32 in decimal, binary, octal, hexadecimal and base 36
Decimal	Binary	Octal	Hex	Base 36
0	0	0	0	0
1	1	1	1	1
2	10	2	2	2
3	11	3	3	3
4	100	4	4	4
5	101	5	5	5
6	110	6	6	6
7	111	7	7	7
8	1000	10	8	8
9	1001	11	9	9
10	1010	12	A	A
11	1011	13	B	B
12	1100	14	C	C
13	1101	15	D	D
14	1110	16	E	E
15	1111	17	F	F
16	10000	20	10	G
17	10001	21	11	H
18	10010	22	12	I
19	10011	23	13	J
20	10100	24	14	K
21	10101	25	15	L
22	10110	26	16	M
23	10111	27	17	N
24	11000	30	18	O
25	11001	31	19	P
26	11010	32	1A	Q
27	11011	33	1B	R
28	11100	34	1C	S
29	11101	35	1D	T
30	11110	36	1E	U
31	11111	37	1F	V
32	100000	40	20	W

Powers of 2 and byte sizes

Powers of 2 are round numbers in binary and hex. The SI prefixes kilo, mega and giga mean powers of 10; the IEC binary prefixes kibi (Ki), mebi (Mi) and gibi (Gi) mean 2¹⁰, 2²⁰ and 2³⁰.

Powers of 2 in decimal, hex and binary prefix
Power	Decimal	Hex	Binary prefix
2⁰	1	1
2¹	2	2
2²	4	4
2³	8	8
2⁴	16	10
2⁷	128	80
2⁸	256	100
2¹⁰	1,024	400	1 Ki (kibi)
2¹⁶	65,536	10000
2²⁰	1,048,576	100000	1 Mi (mebi)
2³⁰	1,073,741,824	40000000	1 Gi (gibi)
2³²	4,294,967,296	100000000

Sources: NIST: Prefixes for binary multiples

Numeral Systems: Binary, Octal, Decimal and Hexadecimal

Place value in any base

Conversion table, 0 to 32

Powers of 2 and byte sizes

References

Frequently asked questions