Binary to Decimal Converter

Q: What is 1010 in decimal?

1010 is 10: the 8 and the 2 places are on, and 8 + 2 = 10.

Q: What is 11111111 in decimal?

11111111 is 255, the largest number one byte can hold. Read as a signed two's complement number, it is -1.

Type a binary number to get its decimal value. The result shows the sum of the place values, and the table under it lists the place value of every bit, so you can check your working.

Binary to decimal

Binary

Signed (two's complement)

Decimal

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How to convert binary to decimal by hand

Each bit has a place value, a power of 2 that doubles from right to left: 1, 2, 4, 8, 16 and so on. Write the place value over each bit, then add up the place values where the bit is 1. Here is 101101 worked out.

How to convert binary to decimal by hand
Bit	Place value	Value
1	2⁵ = 32	32
0	2⁴ = 16	0
1	2³ = 8	8
1	2² = 4	4
0	2¹ = 2	0
1	2⁰ = 1	1

32 + 8 + 4 + 1 = 45

Negative numbers and fractions

Binary has no minus sign, so computers store negative numbers in two's complement: the leftmost bit counts as a negative place value. Read as unsigned, 11111111 is 255. Turn on Signed (two's complement) and the same 8 bits read as -1, because the top bit is worth -128 instead of 128.

Bits after a binary point have place values of one half, one quarter, one eighth and so on. So 101.101 is 4 + 1 + 0.5 + 0.125 = 5.625. The converter gives the exact decimal, even for long binary numbers that go past what a calculator can hold.

Binary to decimal table, 0 to 255

Every value one byte can hold, with its 8-bit binary and hex. Search for a number or a binary pattern.

Search the table

Binary to decimal table, 0 to 255
Decimal	Binary	Hex
0	00000000	00
1	00000001	01
2	00000010	02
3	00000011	03
4	00000100	04
5	00000101	05
6	00000110	06
7	00000111	07
8	00001000	08
9	00001001	09
10	00001010	0A
11	00001011	0B
12	00001100	0C
13	00001101	0D
14	00001110	0E
15	00001111	0F
16	00010000	10
17	00010001	11
18	00010010	12
19	00010011	13
20	00010100	14
21	00010101	15
22	00010110	16
23	00010111	17
24	00011000	18
25	00011001	19
26	00011010	1A
27	00011011	1B
28	00011100	1C
29	00011101	1D
30	00011110	1E
31	00011111	1F
32	00100000	20
33	00100001	21
34	00100010	22
35	00100011	23
36	00100100	24
37	00100101	25
38	00100110	26
39	00100111	27
40	00101000	28
41	00101001	29
42	00101010	2A
43	00101011	2B
44	00101100	2C
45	00101101	2D
46	00101110	2E
47	00101111	2F
48	00110000	30
49	00110001	31
50	00110010	32
51	00110011	33
52	00110100	34
53	00110101	35
54	00110110	36
55	00110111	37
56	00111000	38
57	00111001	39
58	00111010	3A
59	00111011	3B
60	00111100	3C
61	00111101	3D
62	00111110	3E
63	00111111	3F
64	01000000	40
65	01000001	41
66	01000010	42
67	01000011	43
68	01000100	44
69	01000101	45
70	01000110	46
71	01000111	47
72	01001000	48
73	01001001	49
74	01001010	4A
75	01001011	4B
76	01001100	4C
77	01001101	4D
78	01001110	4E
79	01001111	4F
80	01010000	50
81	01010001	51
82	01010010	52
83	01010011	53
84	01010100	54
85	01010101	55
86	01010110	56
87	01010111	57
88	01011000	58
89	01011001	59
90	01011010	5A
91	01011011	5B
92	01011100	5C
93	01011101	5D
94	01011110	5E
95	01011111	5F
96	01100000	60
97	01100001	61
98	01100010	62
99	01100011	63
100	01100100	64
101	01100101	65
102	01100110	66
103	01100111	67
104	01101000	68
105	01101001	69
106	01101010	6A
107	01101011	6B
108	01101100	6C
109	01101101	6D
110	01101110	6E
111	01101111	6F
112	01110000	70
113	01110001	71
114	01110010	72
115	01110011	73
116	01110100	74
117	01110101	75
118	01110110	76
119	01110111	77
120	01111000	78
121	01111001	79
122	01111010	7A
123	01111011	7B
124	01111100	7C
125	01111101	7D
126	01111110	7E
127	01111111	7F
128	10000000	80
129	10000001	81
130	10000010	82
131	10000011	83
132	10000100	84
133	10000101	85
134	10000110	86
135	10000111	87
136	10001000	88
137	10001001	89
138	10001010	8A
139	10001011	8B
140	10001100	8C
141	10001101	8D
142	10001110	8E
143	10001111	8F
144	10010000	90
145	10010001	91
146	10010010	92
147	10010011	93
148	10010100	94
149	10010101	95
150	10010110	96
151	10010111	97
152	10011000	98
153	10011001	99
154	10011010	9A
155	10011011	9B
156	10011100	9C
157	10011101	9D
158	10011110	9E
159	10011111	9F
160	10100000	A0
161	10100001	A1
162	10100010	A2
163	10100011	A3
164	10100100	A4
165	10100101	A5
166	10100110	A6
167	10100111	A7
168	10101000	A8
169	10101001	A9
170	10101010	AA
171	10101011	AB
172	10101100	AC
173	10101101	AD
174	10101110	AE
175	10101111	AF
176	10110000	B0
177	10110001	B1
178	10110010	B2
179	10110011	B3
180	10110100	B4
181	10110101	B5
182	10110110	B6
183	10110111	B7
184	10111000	B8
185	10111001	B9
186	10111010	BA
187	10111011	BB
188	10111100	BC
189	10111101	BD
190	10111110	BE
191	10111111	BF
192	11000000	C0
193	11000001	C1
194	11000010	C2
195	11000011	C3
196	11000100	C4
197	11000101	C5
198	11000110	C6
199	11000111	C7
200	11001000	C8
201	11001001	C9
202	11001010	CA
203	11001011	CB
204	11001100	CC
205	11001101	CD
206	11001110	CE
207	11001111	CF
208	11010000	D0
209	11010001	D1
210	11010010	D2
211	11010011	D3
212	11010100	D4
213	11010101	D5
214	11010110	D6
215	11010111	D7
216	11011000	D8
217	11011001	D9
218	11011010	DA
219	11011011	DB
220	11011100	DC
221	11011101	DD
222	11011110	DE
223	11011111	DF
224	11100000	E0
225	11100001	E1
226	11100010	E2
227	11100011	E3
228	11100100	E4
229	11100101	E5
230	11100110	E6
231	11100111	E7
232	11101000	E8
233	11101001	E9
234	11101010	EA
235	11101011	EB
236	11101100	EC
237	11101101	ED
238	11101110	EE
239	11101111	EF
240	11110000	F0
241	11110001	F1
242	11110010	F2
243	11110011	F3
244	11110100	F4
245	11110101	F5
246	11110110	F6
247	11110111	F7
248	11111000	F8
249	11111001	F9
250	11111010	FA
251	11111011	FB
252	11111100	FC
253	11111101	FD
254	11111110	FE
255	11111111	FF

Frequently asked questions

How do you convert binary to decimal by hand?

Write the powers of 2 above the bits, starting with 1 on the right and doubling as you go left. Add the powers that sit over a 1. For `1101`, that is 8 + 4 + 1 = 13.

What is 1010 in decimal?

`1010` is 10: the 8 and the 2 places are on, and 8 + 2 = 10.

What is 11111111 in decimal?

`11111111` is 255, the largest number one byte can hold. Read as a signed two's complement number, it is -1.

How does two's complement work?

The leftmost bit counts as negative. In 8 bits it is worth -128, so `11111011` is -128 + 64 + 32 + 16 + 8 + 2 + 1 = -5. To negate a number, flip every bit and add 1. Turn on Signed (two's complement) above to read binary this way.