Binary to Decimal Converter

Type a binary number and its decimal value appears instantly as you type — no Convert button anywhere on this page. Every other base updates at the same time, and the place-value working for your exact number is shown underneath.

Convert Binary to Decimal

Binary₂ (from)

Only 0–1. Type here — the answer appears instantly, no button to press.

Decimal₁₀ (to)

Quinary₅

Octal₈

Hexadecimal₁₆

Type a number in any box above.

How to convert binary to decimal

Label the place values. Starting from the rightmost bit, write 1, 2, 4, 8, 16… doubling each step to the left. These are the powers of 2: 2⁰, 2¹, 2², 2³…
Keep only the 1 bits. A 1 bit earns its full place value; a 0 bit earns nothing — but it still holds its position.
Add the place values together. The total is the decimal number.

The loop, visually

Example: 101010₂: 1×32 = 32 → +0×16 = 32 → +1×8 = 40 → +0×4 = 40 → +1×2 = 42 → +0×1 = 42₁₀

One loop per bit: a 1 bit adds its full place value to the total; a 0 bit adds nothing, but it still holds its place.

That is all there is to it — and the converter above writes out this expansion live for any binary number you enter.

Worked example: 101010₂ = 42₁₀

Bit	Position	Place value	Bit × place
1	5	32	32
0	4	16	0
1	3	8	8
0	2	4	0
1	1	2	2
0	0	1	0

Add the last column: 32 + 8 + 2 = 42. So 101010₂ = 42₁₀.

Worked example: 1101₂ = 13₁₀

The 1 bits of 1101 sit at place values 8, 4 and 1. Adding them: 8 + 4 + 1 = 13. Notice the 0 bit in the 2s place contributes nothing but still shifts the other bits one place higher.

Binary to decimal conversion table (0–255)

Every byte value from 0 to 255 in binary, decimal, octal and hexadecimal.

Decimal₁₀	Binary₂	Octal₈	Hexadecimal₁₆
0	0	0	0
1	1	1	1
2	10	2	2
3	11	3	3
4	100	4	4
5	101	5	5
6	110	6	6
7	111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F
16	10000	20	10
17	10001	21	11
18	10010	22	12
19	10011	23	13
20	10100	24	14
21	10101	25	15
22	10110	26	16
23	10111	27	17
24	11000	30	18
25	11001	31	19
26	11010	32	1A
27	11011	33	1B
28	11100	34	1C
29	11101	35	1D
30	11110	36	1E
31	11111	37	1F
32	100000	40	20
33	100001	41	21
34	100010	42	22
35	100011	43	23
36	100100	44	24
37	100101	45	25
38	100110	46	26
39	100111	47	27
40	101000	50	28
41	101001	51	29
42	101010	52	2A
43	101011	53	2B
44	101100	54	2C
45	101101	55	2D
46	101110	56	2E
47	101111	57	2F
48	110000	60	30
49	110001	61	31
50	110010	62	32
51	110011	63	33
52	110100	64	34
53	110101	65	35
54	110110	66	36
55	110111	67	37
56	111000	70	38
57	111001	71	39
58	111010	72	3A
59	111011	73	3B
60	111100	74	3C
61	111101	75	3D
62	111110	76	3E
63	111111	77	3F
64	1000000	100	40
65	1000001	101	41
66	1000010	102	42
67	1000011	103	43
68	1000100	104	44
69	1000101	105	45
70	1000110	106	46
71	1000111	107	47
72	1001000	110	48
73	1001001	111	49
74	1001010	112	4A
75	1001011	113	4B
76	1001100	114	4C
77	1001101	115	4D
78	1001110	116	4E
79	1001111	117	4F
80	1010000	120	50
81	1010001	121	51
82	1010010	122	52
83	1010011	123	53
84	1010100	124	54
85	1010101	125	55
86	1010110	126	56
87	1010111	127	57
88	1011000	130	58
89	1011001	131	59
90	1011010	132	5A
91	1011011	133	5B
92	1011100	134	5C
93	1011101	135	5D
94	1011110	136	5E
95	1011111	137	5F
96	1100000	140	60
97	1100001	141	61
98	1100010	142	62
99	1100011	143	63
100	1100100	144	64
101	1100101	145	65
102	1100110	146	66
103	1100111	147	67
104	1101000	150	68
105	1101001	151	69
106	1101010	152	6A
107	1101011	153	6B
108	1101100	154	6C
109	1101101	155	6D
110	1101110	156	6E
111	1101111	157	6F
112	1110000	160	70
113	1110001	161	71
114	1110010	162	72
115	1110011	163	73
116	1110100	164	74
117	1110101	165	75
118	1110110	166	76
119	1110111	167	77
120	1111000	170	78
121	1111001	171	79
122	1111010	172	7A
123	1111011	173	7B
124	1111100	174	7C
125	1111101	175	7D
126	1111110	176	7E
127	1111111	177	7F
128	10000000	200	80
129	10000001	201	81
130	10000010	202	82
131	10000011	203	83
132	10000100	204	84
133	10000101	205	85
134	10000110	206	86
135	10000111	207	87
136	10001000	210	88
137	10001001	211	89
138	10001010	212	8A
139	10001011	213	8B
140	10001100	214	8C
141	10001101	215	8D
142	10001110	216	8E
143	10001111	217	8F
144	10010000	220	90
145	10010001	221	91
146	10010010	222	92
147	10010011	223	93
148	10010100	224	94
149	10010101	225	95
150	10010110	226	96
151	10010111	227	97
152	10011000	230	98
153	10011001	231	99
154	10011010	232	9A
155	10011011	233	9B
156	10011100	234	9C
157	10011101	235	9D
158	10011110	236	9E
159	10011111	237	9F
160	10100000	240	A0
161	10100001	241	A1
162	10100010	242	A2
163	10100011	243	A3
164	10100100	244	A4
165	10100101	245	A5
166	10100110	246	A6
167	10100111	247	A7
168	10101000	250	A8
169	10101001	251	A9
170	10101010	252	AA
171	10101011	253	AB
172	10101100	254	AC
173	10101101	255	AD
174	10101110	256	AE
175	10101111	257	AF
176	10110000	260	B0
177	10110001	261	B1
178	10110010	262	B2
179	10110011	263	B3
180	10110100	264	B4
181	10110101	265	B5
182	10110110	266	B6
183	10110111	267	B7
184	10111000	270	B8
185	10111001	271	B9
186	10111010	272	BA
187	10111011	273	BB
188	10111100	274	BC
189	10111101	275	BD
190	10111110	276	BE
191	10111111	277	BF
192	11000000	300	C0
193	11000001	301	C1
194	11000010	302	C2
195	11000011	303	C3
196	11000100	304	C4
197	11000101	305	C5
198	11000110	306	C6
199	11000111	307	C7
200	11001000	310	C8
201	11001001	311	C9
202	11001010	312	CA
203	11001011	313	CB
204	11001100	314	CC
205	11001101	315	CD
206	11001110	316	CE
207	11001111	317	CF
208	11010000	320	D0
209	11010001	321	D1
210	11010010	322	D2
211	11010011	323	D3
212	11010100	324	D4
213	11010101	325	D5
214	11010110	326	D6
215	11010111	327	D7
216	11011000	330	D8
217	11011001	331	D9
218	11011010	332	DA
219	11011011	333	DB
220	11011100	334	DC
221	11011101	335	DD
222	11011110	336	DE
223	11011111	337	DF
224	11100000	340	E0
225	11100001	341	E1
226	11100010	342	E2
227	11100011	343	E3
228	11100100	344	E4
229	11100101	345	E5
230	11100110	346	E6
231	11100111	347	E7
232	11101000	350	E8
233	11101001	351	E9
234	11101010	352	EA
235	11101011	353	EB
236	11101100	354	EC
237	11101101	355	ED
238	11101110	356	EE
239	11101111	357	EF
240	11110000	360	F0
241	11110001	361	F1
242	11110010	362	F2
243	11110011	363	F3
244	11110100	364	F4
245	11110101	365	F5
246	11110110	366	F6
247	11110111	367	F7
248	11111000	370	F8
249	11111001	371	F9
250	11111010	372	FA
251	11111011	373	FB
252	11111100	374	FC
253	11111101	375	FD
254	11111110	376	FE
255	11111111	377	FF

Frequently asked questions

How do I convert binary to decimal?

Give each bit a place value: the rightmost bit is worth 1, then 2, 4, 8, 16 and so on, doubling each step left. Add up the place values wherever the bit is 1. The converter above shows this expansion live for the exact binary number you type.

What is 101010 in decimal?

101010 in decimal is 42. The 1 bits sit at place values 32, 8 and 2, and 32 + 8 + 2 = 42.

What is 11111111 in decimal?

11111111 in decimal is 255: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. Eight 1 bits always give 2⁸ − 1.

Do the zeros in a binary number matter?

Yes — a 0 bit contributes nothing to the sum, but it still holds a position, pushing the 1 bits to its left into higher place values. 101 (5) and 1001 (9) differ only because of where the zeros sit.

How can I check a binary to decimal conversion?

Convert the decimal answer back to binary (divide by 2, read the remainders bottom to top) and see whether you land on the original bits. Or type the binary number above and compare — RadixFlip shows both directions at once.

What is 10101 in decimal?

10101 in decimal is 21: the 1 bits sit at place values 16, 4 and 1, and 16 + 4 + 1 = 21. See the full place-value steps for 10101 in decimal.

What is 1111 in decimal?

1111 in decimal is 15: 8 + 4 + 2 + 1 = 15 — four 1 bits always add up to 2⁴ − 1. See the full place-value steps for 1111 in decimal.

What is 1010 in decimal?

1010 in decimal is 10: the 1 bits sit at place values 8 and 2, and 8 + 2 = 10. See the full place-value steps for 1010 in decimal.

Binary to Decimal Converter

Convert Binary to Decimal

See the steps for your number

How to convert binary to decimal

The loop, visually

Worked example: 101010₂ = 42₁₀

Worked example: 1101₂ = 13₁₀

Binary to decimal conversion table (0–255)

Frequently asked questions

Popular values

See also

Number base converters

Text & ASCII converters

Calculators & tools