Binary, Decimal, Hex & Octal Converter

One converter for every number base

Choose what you are converting from and to, then type. The result you asked for appears in the highlighted box, and every other representation (binary, octal, decimal, hexadecimal, a custom base, text and Base64) is listed underneath, so you rarely need a second tool. Values of any length are converted exactly: a 300-digit decimal number or a 4,000-bit hex string is no problem, because the converter uses arbitrary-precision integers rather than JavaScript’s 53-bit numbers. Invalid digits are reported with their position, for example a 2 in a binary number or a G in hex.

How positional notation works

Every base works the same way. A number is a row of digits, and each position is worth the base raised to a power, counting from 0 on the right. In decimal (base 10) the number 347 means 3×100 + 4×10 + 7×1. In binary (base 2) the positions are worth 1, 2, 4, 8, 16 and so on, so 1011 means 1×8 + 0×4 + 1×2 + 1×1 = 11. Octal uses powers of 8 and the digits 0–7; hexadecimal uses powers of 16 and needs six extra digits, A–F, for the values 10–15. Bases above 16 simply continue through the alphabet, up to base 36, where Z means 35.

Worked examples for each conversion

Binary to decimal

Multiply each bit by its place value and add. For 110101: 32 + 16 + 0 + 4 + 0 + 1 = 53. A quicker way for long numbers is doubling: start at 0 and, for each bit from the left, double the total and add the bit (0→1→3→6→13→26→53).

Decimal to binary, octal and hex

Divide repeatedly by the target base and read the remainders from bottom to top. 53 ÷ 2 gives remainders 1, 0, 1, 0, 1, 1, so 53 = 110101. The same method with 8 gives 65, and with 16 gives 35. For 3735928559 ÷ 16 the remainders spell DEADBEEF.

Binary to hex and octal (and back)

No arithmetic is needed. Each hex digit is exactly four bits and each octal digit exactly three, so split the binary number into groups from the right: 1101 0101 is D5 in hex, and 11 010 101 is 325 in octal. To go back, expand each hex digit to four bits (F → 1111, 7 → 0111) or each octal digit to three.

Hex to decimal and octal

Hex 2F is 2×16 + 15 = 47. To reach octal, the easiest route is through binary: 2F = 0010 1111 = 101 111 = 57. Octal to hex works the same way in reverse.

Octal to decimal

Octal 755, the familiar Unix permission, is 7×64 + 5×8 + 5 = 493. Each octal digit is also one permission group: 7 = rwx, 5 = r-x.

Decimal to ASCII

Enter several decimal codes separated by spaces or commas and each one becomes a character: 72 101 108 108 111 reads Hello. Values above 127 are treated as Unicode code points, so 233 is é and 128512 is 😀.

Base64 to binary, hex and octal

Base64 is not a number base in the usual sense; it is a way of writing bytes with 64 printable characters. Choose Base64 as the input and the tool decodes it to bytes and shows each byte in binary, hex and octal: SGVsbG8= is the five bytes 48 65 6C 6C 6F, which is the text “Hello”.

Binary and hex to Base64

Going the other way, a binary string is cut into bytes (eight bits each, padded on the left) and a hex string into pairs of digits, and those bytes are encoded. 48656C6C6F in hex becomes SGVsbG8=. Leading zero bytes are kept, so 0001 in hex encodes as AAE=.

Negative numbers and two’s complement

Computers store signed integers in two’s complement: a negative number −n in a w-bit field is stored as 2^w − n. In 8 bits, −5 is 256 − 5 = 251 = 11111011 = FB. The top bit doubles as a sign bit, and adding numbers works the same whether they are signed or not. Choose 8, 16, 32 or 64 bits in Signed to see the stored bit pattern of a negative decimal, or to read a binary or hex pattern such as FFFFFFFE as a signed value (−2 in 32 bits). The tool also shows the unsigned reading and warns when a value does not fit, for example −129 in 8 bits, whose range is −128 to 127. With Signed off, negative numbers are simply written with a minus sign in every base.

Fractions: decimal to binary

For the part after the point, multiply by the target base and take the whole-number part as the next digit. 0.625 × 2 = 1.25 (digit 1), 0.25 × 2 = 0.5 (digit 0), 0.5 × 2 = 1.0 (digit 1), so 10.625 = 1010.101. Many decimal fractions never end in binary: 0.1 becomes 0.000110011001100… repeating forever, which is why 0.1 + 0.2 is not exactly 0.3 in most programming languages. Set Fraction digits to choose where to stop; a trailing … tells you the result was cut off. Fractional binary, octal and hex inputs convert back to exact decimals.

Grouping, case and multiple values

Long binary numbers are easier to read in groups: choose nibbles (four bits, one hex digit) or bytes (eight bits). Hex can be shown in upper or lower case. Spaces and commas in the input are treated automatically: in decimal they separate several values, while in binary and hex they are assumed to be digit grouping inside one number. Change Spaces and commas to override that. Links such as ?mode=binary-to-decimal or ?mode=decimal-to-ascii open the converter with that pair already chosen.

Conversion table 0–255

The first 16 values are worth memorizing; the full byte range is in the expandable table below.

Show the full 0–255 conversion table (decimal, hex, octal, binary, ASCII)

Dec	Hex	Oct	Binary	ASCII
0	00	000	00000000	NUL
1	01	001	00000001
2	02	002	00000010
3	03	003	00000011
4	04	004	00000100
5	05	005	00000101
6	06	006	00000110
7	07	007	00000111
8	08	010	00001000
9	09	011	00001001	TAB
10	0A	012	00001010	LF
11	0B	013	00001011
12	0C	014	00001100
13	0D	015	00001101	CR
14	0E	016	00001110
15	0F	017	00001111
16	10	020	00010000
17	11	021	00010001
18	12	022	00010010
19	13	023	00010011
20	14	024	00010100
21	15	025	00010101
22	16	026	00010110
23	17	027	00010111
24	18	030	00011000
25	19	031	00011001
26	1A	032	00011010
27	1B	033	00011011
28	1C	034	00011100
29	1D	035	00011101
30	1E	036	00011110
31	1F	037	00011111
32	20	040	00100000	space
33	21	041	00100001	!
34	22	042	00100010	"
35	23	043	00100011	#
36	24	044	00100100	$
37	25	045	00100101	%
38	26	046	00100110	&
39	27	047	00100111	'
40	28	050	00101000	(
41	29	051	00101001	)
42	2A	052	00101010	*
43	2B	053	00101011	+
44	2C	054	00101100	,
45	2D	055	00101101	-
46	2E	056	00101110	.
47	2F	057	00101111	/
48	30	060	00110000	0
49	31	061	00110001	1
50	32	062	00110010	2
51	33	063	00110011	3
52	34	064	00110100	4
53	35	065	00110101	5
54	36	066	00110110	6
55	37	067	00110111	7
56	38	070	00111000	8
57	39	071	00111001	9
58	3A	072	00111010	:
59	3B	073	00111011	;
60	3C	074	00111100	<
61	3D	075	00111101	=
62	3E	076	00111110	>
63	3F	077	00111111	?
64	40	100	01000000	@
65	41	101	01000001	A
66	42	102	01000010	B
67	43	103	01000011	C
68	44	104	01000100	D
69	45	105	01000101	E
70	46	106	01000110	F
71	47	107	01000111	G
72	48	110	01001000	H
73	49	111	01001001	I
74	4A	112	01001010	J
75	4B	113	01001011	K
76	4C	114	01001100	L
77	4D	115	01001101	M
78	4E	116	01001110	N
79	4F	117	01001111	O
80	50	120	01010000	P
81	51	121	01010001	Q
82	52	122	01010010	R
83	53	123	01010011	S
84	54	124	01010100	T
85	55	125	01010101	U
86	56	126	01010110	V
87	57	127	01010111	W
88	58	130	01011000	X
89	59	131	01011001	Y
90	5A	132	01011010	Z
91	5B	133	01011011	[
92	5C	134	01011100	\
93	5D	135	01011101	]
94	5E	136	01011110	^
95	5F	137	01011111	_
96	60	140	01100000	`
97	61	141	01100001	a
98	62	142	01100010	b
99	63	143	01100011	c
100	64	144	01100100	d
101	65	145	01100101	e
102	66	146	01100110	f
103	67	147	01100111	g
104	68	150	01101000	h
105	69	151	01101001	i
106	6A	152	01101010	j
107	6B	153	01101011	k
108	6C	154	01101100	l
109	6D	155	01101101	m
110	6E	156	01101110	n
111	6F	157	01101111	o
112	70	160	01110000	p
113	71	161	01110001	q
114	72	162	01110010	r
115	73	163	01110011	s
116	74	164	01110100	t
117	75	165	01110101	u
118	76	166	01110110	v
119	77	167	01110111	w
120	78	170	01111000	x
121	79	171	01111001	y
122	7A	172	01111010	z
123	7B	173	01111011	{
124	7C	174	01111100	|
125	7D	175	01111101	}
126	7E	176	01111110	~
127	7F	177	01111111	DEL
128	80	200	10000000	·
129	81	201	10000001	·
130	82	202	10000010	·
131	83	203	10000011	·
132	84	204	10000100	·
133	85	205	10000101	·
134	86	206	10000110	·
135	87	207	10000111	·
136	88	210	10001000	·
137	89	211	10001001	·
138	8A	212	10001010	·
139	8B	213	10001011	·
140	8C	214	10001100	·
141	8D	215	10001101	·
142	8E	216	10001110	·
143	8F	217	10001111	·
144	90	220	10010000	·
145	91	221	10010001	·
146	92	222	10010010	·
147	93	223	10010011	·
148	94	224	10010100	·
149	95	225	10010101	·
150	96	226	10010110	·
151	97	227	10010111	·
152	98	230	10011000	·
153	99	231	10011001	·
154	9A	232	10011010	·
155	9B	233	10011011	·
156	9C	234	10011100	·
157	9D	235	10011101	·
158	9E	236	10011110	·
159	9F	237	10011111	·
160	A0	240	10100000	·
161	A1	241	10100001	·
162	A2	242	10100010	·
163	A3	243	10100011	·
164	A4	244	10100100	·
165	A5	245	10100101	·
166	A6	246	10100110	·
167	A7	247	10100111	·
168	A8	250	10101000	·
169	A9	251	10101001	·
170	AA	252	10101010	·
171	AB	253	10101011	·
172	AC	254	10101100	·
173	AD	255	10101101	·
174	AE	256	10101110	·
175	AF	257	10101111	·
176	B0	260	10110000	·
177	B1	261	10110001	·
178	B2	262	10110010	·
179	B3	263	10110011	·
180	B4	264	10110100	·
181	B5	265	10110101	·
182	B6	266	10110110	·
183	B7	267	10110111	·
184	B8	270	10111000	·
185	B9	271	10111001	·
186	BA	272	10111010	·
187	BB	273	10111011	·
188	BC	274	10111100	·
189	BD	275	10111101	·
190	BE	276	10111110	·
191	BF	277	10111111	·
192	C0	300	11000000	·
193	C1	301	11000001	·
194	C2	302	11000010	·
195	C3	303	11000011	·
196	C4	304	11000100	·
197	C5	305	11000101	·
198	C6	306	11000110	·
199	C7	307	11000111	·
200	C8	310	11001000	·
201	C9	311	11001001	·
202	CA	312	11001010	·
203	CB	313	11001011	·
204	CC	314	11001100	·
205	CD	315	11001101	·
206	CE	316	11001110	·
207	CF	317	11001111	·
208	D0	320	11010000	·
209	D1	321	11010001	·
210	D2	322	11010010	·
211	D3	323	11010011	·
212	D4	324	11010100	·
213	D5	325	11010101	·
214	D6	326	11010110	·
215	D7	327	11010111	·
216	D8	330	11011000	·
217	D9	331	11011001	·
218	DA	332	11011010	·
219	DB	333	11011011	·
220	DC	334	11011100	·
221	DD	335	11011101	·
222	DE	336	11011110	·
223	DF	337	11011111	·
224	E0	340	11100000	·
225	E1	341	11100001	·
226	E2	342	11100010	·
227	E3	343	11100011	·
228	E4	344	11100100	·
229	E5	345	11100101	·
230	E6	346	11100110	·
231	E7	347	11100111	·
232	E8	350	11101000	·
233	E9	351	11101001	·
234	EA	352	11101010	·
235	EB	353	11101011	·
236	EC	354	11101100	·
237	ED	355	11101101	·
238	EE	356	11101110	·
239	EF	357	11101111	·
240	F0	360	11110000	·
241	F1	361	11110001	·
242	F2	362	11110010	·
243	F3	363	11110011	·
244	F4	364	11110100	·
245	F5	365	11110101	·
246	F6	366	11110110	·
247	F7	367	11110111	·
248	F8	370	11111000	·
249	F9	371	11111001	·
250	FA	372	11111010	·
251	FB	373	11111011	·
252	FC	374	11111100	·
253	FD	375	11111101	·
254	FE	376	11111110	·
255	FF	377	11111111	·

Frequently asked questions