Binary, Hex & Decimal Converter

Type a number in any box and the others change as you type: binary, octal, decimal and hex, with the working shown. Switch to Advanced for any base up to 36, fractions, two’s complement, bitwise maths, text to binary and a bit grid you can click.

Any base, fractions, signed, bitwise, text, bit grid

Binary (base 2)

Octal (base 8)

Decimal (base 10)

Hex (base 16)

Any base (2 to 36)

Prefixes like 0b, 0o and 0x, spaces and underscores are fine. Use a minus sign for negatives and a point for fractions, like 1010.101.

Group digits

Between groups

Prefixes (0b, 0o, 0x)

Hex letters

Digits after the point

ResultUpdates as you type—Bits needed—Bytes—Number of 1 bits—Smallest type it fitsWorking

More tools

Word size

Uses the whole-number part of the number in the boxes above. Type a negative number like −5 to see how it is stored.

—Two’s complement (binary)—Two’s complement (hex)—These bits read as signed—These bits read as unsigned—Signed range—Unsigned range—One’s complement—Sign and magnitude

Codes 0 to 127. The row for the whole number in the boxes above is highlighted when it is in this range.

Dec	Hex	Binary	Octal	Character
0	00	00000000	000	NUL
1	01	00000001	001	SOH
2	02	00000010	002	STX
3	03	00000011	003	ETX
4	04	00000100	004	EOT
5	05	00000101	005	ENQ
6	06	00000110	006	ACK
7	07	00000111	007	BEL
8	08	00001000	010	BS
9	09	00001001	011	TAB
10	0A	00001010	012	LF
11	0B	00001011	013	VT
12	0C	00001100	014	FF
13	0D	00001101	015	CR
14	0E	00001110	016	SO
15	0F	00001111	017	SI
16	10	00010000	020	DLE
17	11	00010001	021	DC1
18	12	00010010	022	DC2
19	13	00010011	023	DC3
20	14	00010100	024	DC4
21	15	00010101	025	NAK
22	16	00010110	026	SYN
23	17	00010111	027	ETB
24	18	00011000	030	CAN
25	19	00011001	031	EM
26	1A	00011010	032	SUB
27	1B	00011011	033	ESC
28	1C	00011100	034	FS
29	1D	00011101	035	GS
30	1E	00011110	036	RS
31	1F	00011111	037	US
32	20	00100000	040	Space
33	21	00100001	041	!
34	22	00100010	042	"
35	23	00100011	043	#
36	24	00100100	044	$
37	25	00100101	045	%
38	26	00100110	046	&
39	27	00100111	047	'
40	28	00101000	050	(
41	29	00101001	051	)
42	2A	00101010	052	*
43	2B	00101011	053	+
44	2C	00101100	054	,
45	2D	00101101	055	-
46	2E	00101110	056	.
47	2F	00101111	057	/
48	30	00110000	060	0
49	31	00110001	061	1
50	32	00110010	062	2
51	33	00110011	063	3
52	34	00110100	064	4
53	35	00110101	065	5
54	36	00110110	066	6
55	37	00110111	067	7
56	38	00111000	070	8
57	39	00111001	071	9
58	3A	00111010	072	:
59	3B	00111011	073	;
60	3C	00111100	074	<
61	3D	00111101	075	=
62	3E	00111110	076	>
63	3F	00111111	077	?
64	40	01000000	100	@
65	41	01000001	101	A
66	42	01000010	102	B
67	43	01000011	103	C
68	44	01000100	104	D
69	45	01000101	105	E
70	46	01000110	106	F
71	47	01000111	107	G
72	48	01001000	110	H
73	49	01001001	111	I
74	4A	01001010	112	J
75	4B	01001011	113	K
76	4C	01001100	114	L
77	4D	01001101	115	M
78	4E	01001110	116	N
79	4F	01001111	117	O
80	50	01010000	120	P
81	51	01010001	121	Q
82	52	01010010	122	R
83	53	01010011	123	S
84	54	01010100	124	T
85	55	01010101	125	U
86	56	01010110	126	V
87	57	01010111	127	W
88	58	01011000	130	X
89	59	01011001	131	Y
90	5A	01011010	132	Z
91	5B	01011011	133	[
92	5C	01011100	134	\
93	5D	01011101	135	]
94	5E	01011110	136	^
95	5F	01011111	137	_
96	60	01100000	140	`
97	61	01100001	141	a
98	62	01100010	142	b
99	63	01100011	143	c
100	64	01100100	144	d
101	65	01100101	145	e
102	66	01100110	146	f
103	67	01100111	147	g
104	68	01101000	150	h
105	69	01101001	151	i
106	6A	01101010	152	j
107	6B	01101011	153	k
108	6C	01101100	154	l
109	6D	01101101	155	m
110	6E	01101110	156	n
111	6F	01101111	157	o
112	70	01110000	160	p
113	71	01110001	161	q
114	72	01110010	162	r
115	73	01110011	163	s
116	74	01110100	164	t
117	75	01110101	165	u
118	76	01110110	166	v
119	77	01110111	167	w
120	78	01111000	170	x
121	79	01111001	171	y
122	7A	01111010	172	z
123	7B	01111011	173	{
124	7C	01111100	174	\|
125	7D	01111101	175	}
126	7E	01111110	176	~
127	7F	01111111	177	DEL

How your number is converted

Your number, step by step: divide by 2, read the remainders, then group the bits into hex.

1
Divide by 2
173 ÷ 2 = 86 r 1
8 divisions
2
Read remainders up
binary 1010 1101
3
Fours make hex
1010 1101
hex AD
4
Check place values
128+32+8+4+1
= 173

Read more: the formula, a worked example, two’s complement and tables

Every number system works the same way: each place is worth the base times the place to its right. In decimal the places are 1, 10, 100, 1000. In binary (base 2) they are 1, 2, 4, 8, 16. In hex (base 16) they are 1, 16, 256, 4096, and the digits run 0–9 then A–F for 10 to 15. Octal (base 8) uses the digits 0–7. Computers store everything as bits (0s and 1s); hex and octal are short ways to write those bits, because one hex digit is exactly four bits and one octal digit is exactly three.

The formula

To base b: divide by b, write down the remainder, repeat with the answer until it is 0; the digits are the remainders read from last to first
From base b: value = (each digit × b to the power of its place), added up; places count 0, 1, 2… from the right of the point, and −1, −2… after it
Fraction part to base b: multiply by b; the whole part is the next digit; repeat with what is left
Binary ↔ hex: 4 bits = 1 hex digit. Binary ↔ octal: 3 bits = 1 octal digit
Two’s complement of −x in n bits = 2ⁿ − x (flip every bit of x, then add 1)

Worked example

173 to binary. Divide by 2 and keep the remainders: 173 ÷ 2 = 86 r 1, 86 ÷ 2 = 43 r 0, 43 ÷ 2 = 21 r 1, 21 ÷ 2 = 10 r 1, 10 ÷ 2 = 5 r 0, 5 ÷ 2 = 2 r 1, 2 ÷ 2 = 1 r 0, 1 ÷ 2 = 0 r 1. Read from the last remainder to the first: 10101101.

Check with place values. 10101101 has 1s in the 128, 32, 8, 4 and 1 places: 128 + 32 + 8 + 4 + 1 = 173.

To hex. Split into fours: 1010 1101. 1010 = 8 + 2 = 10 = A and 1101 = 8 + 4 + 1 = 13 = D, so 173 = AD in hex. Check: 10 × 16 + 13 = 160 + 13 = 173.

To octal. Split into threes from the right: 010 101 101 = 2, 5, 5, so 173 = 255 in octal. Check: 2 × 64 + 5 × 8 + 5 = 128 + 40 + 5 = 173.

Fractions

10.625 to binary: the whole part 10 is 1010. For the fraction part, multiply by 2 and take the whole part each time: 0.625 × 2 = 1.25 → 1, 0.25 × 2 = 0.5 → 0, 0.5 × 2 = 1.0 → 1, and nothing is left. So 10.625 = 1010.101. Going back: 8 + 2 + 0.5 + 0.125 = 10.625. Some fractions never end in another base: 0.1 in binary is 0.0001100110011… with 0011 repeating for ever, which is why computers cannot store 0.1 exactly. The converter stops at the number of digits you choose, shows … when it has cut a number short, and names the repeating block.

Negative numbers: two’s complement

Computers store negative whole numbers in two’s complement. To write −5 in 8 bits: 5 is 00000101, flip every bit to get 11111010, then add 1 to get 11111011 (FB in hex). This is the same as 2⁸ − 5 = 256 − 5 = 251. The left-most bit is the sign bit: 1 means negative. Read 11111011 as unsigned and it is 251; read it as signed and it is −5. If a number is too big for the word size it overflows: in 8 bits, 200 read as signed is 200 − 256 = −56.

Word size	Signed range	Unsigned range
8 bits (byte)	−128 to 127	0 to 255
16 bits	−32,768 to 32,767	0 to 65,535
32 bits	−2,147,483,648 to 2,147,483,647	0 to 4,294,967,295
64 bits	−9,223,372,036,854,775,808 to 9,223,372,036,854,775,807	0 to 18,446,744,073,709,551,615

Bitwise operations

AND gives 1 only where both bits are 1: 1100 AND 1010 = 1000 (12 AND 10 = 8).
OR gives 1 where either bit is 1: 1100 OR 1010 = 1110 (14). XOR gives 1 where the bits differ: 0110 (6).
NOT flips every bit in the word size: NOT 00001100 = 11110011 (243 in 8 bits). NAND, NOR and XNOR are NOT of AND, OR and XOR.
Shift left by k doubles the number k times, dropping bits that fall off the left. Shift right halves it, dropping bits off the right. An arithmetic right shift copies the sign bit in, so negative numbers stay negative. Rotate moves the bits that fall off one end back in at the other.

Hex digits and their bits

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

Powers of 2

Power	Value	Power	Value
2⁰	1	2⁸	256
2¹	2	2⁹	512
2²	4	2¹⁰	1,024
2³	8	2¹¹	2,048
2⁴	16	2¹²	4,096
2⁵	32	2¹³	8,192
2⁶	64	2¹⁴	16,384
2⁷	128	2¹⁵	32,768
2³²	4,294,967,296	2⁶⁴	18,446,744,073,709,551,616

Text to binary

Text is stored as bytes. This page uses UTF-8, the encoding used by almost every web page. English letters, digits and common symbols (the ASCII set, codes 0–127) take one byte each, so “Hi” is 72 105, or 01001000 01101001 in binary. Accented letters take two bytes, the euro sign € takes three (E2 82 AC) and most emoji take four.

All maths is exact: the converter uses whole numbers of any size (up to 4,000 characters per box) and exact fractions, so there are no rounding errors until a fraction is cut short at the number of digits you choose.

Common questions

How do I convert decimal to binary?

Divide the number by 2 and write down the remainder (0 or 1). Divide the answer by 2 again and keep going until you reach 0. Read the remainders from the last one to the first. For 173: 173 ÷ 2 = 86 r 1, 86 ÷ 2 = 43 r 0 and so on, which gives 10101101.

How do I convert binary to decimal?

Each place in a binary number is worth twice the place to its right: 1, 2, 4, 8, 16 and so on. Add up the places that hold a 1. For 10101101 that is 128 + 32 + 8 + 4 + 1 = 173.

How do I convert hex to decimal?

Hex digits run 0–9 then A = 10, B = 11, up to F = 15, and each place is worth 16 times the place to its right. Multiply each digit by its place value and add: AD = 10 × 16 + 13 × 1 = 173.

How do I convert binary to hex?

Split the bits into groups of four, starting from the right, and add zeros on the left if needed. Each group of four is one hex digit: 1010 = A and 1101 = D, so 10101101 is AD. For octal, use groups of three instead: 010 101 101 = 255.

What is two’s complement?

It is how computers store negative whole numbers. To write −x in n bits, write x in binary, flip every bit and add 1. In 8 bits, 5 is 00000101, flipped it is 11111010, and adding 1 gives 11111011 for −5. An 8-bit signed number runs from −128 to 127.

How do I convert text to binary?

Each character is turned into bytes (UTF-8), and each byte is written as 8 bits. “Hi” is the bytes 72 and 105, which are 01001000 01101001 in binary or 48 69 in hex. Plain English letters take one byte each; a character like € takes three bytes (E2 82 AC).

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Binary, Hex & Decimal Converter

How your number is converted

Divide by 2

Read remainders up

Fours make hex

Check place values

The formula

Worked example

Fractions

Negative numbers: two’s complement

Bitwise operations

Hex digits and their bits

Powers of 2

Text to binary

Common questions

Related calculators

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