Binary to Decimal Converter

Q: What is the difference between a binary number and binary text?

A binary number is a value in base 2 — 01001000 means 72. Binary text is the same bits read as character codes — 01001000 means the letter H. If you want letters, use our binary to text converter; if you want the value, you are in the right place.

Q: What do 0b and 0x prefixes mean?

0b marks a binary literal and 0x marks hexadecimal in programming languages. Both are notation, not part of the value — this converter accepts a 0b prefix and shows the hex spelling of every result.

Convert between binary and decimal in both directions — fractions, signed values and very long numbers included, with the working shown step by step.

Written by Alex Rivera · Last verified: 2026-09-07

Numbers vs text: as a number, 01001000 is 72 — that conversion belongs here. As text, the same bits are the letter H — that belongs to our binary to text converter. Numbers accept any length; text needs complete 8-bit bytes.

Your input — one value per line for batch conversion

Result

Signed (two’s complement)

Waiting for input — conversion happens instantly in your browser.

How to Convert Binary to Decimal by Hand

Two classic methods for whole numbers, one more for fractions — all three are exactly what the converter shows in its step-by-step working.

The positional method (read binary → decimal)

Each bit is worth a power of two, doubling from right to left: 1, 2, 4, 8, 16… Add the values where you see a 1. For 1101: 8 + 4 + 1 = 13. This is the fastest way to read a value.

Double dabble (write decimal → binary)

To write a decimal number in binary, repeatedly halve it and record the remainders. For 13: 13 is odd → 1; 6 is even → 0; 3 is odd → 1; 1 is odd → 1. Reading the remainders bottom to top gives 1101. Same answer, opposite direction.

Fractions: the ×2 method

After the binary point, digits are worth 1/2, 1/4, 1/8… — so 101.11 is 5 + 0.5 + 0.25 = 5.75. Going the other way, multiply the fraction by 2 and take the integer part each time: 0.75 × 2 = 1.5 → 1; 0.5 × 2 = 1.0 → 1; 0 → stop, giving .11. Some decimal fractions (like 0.1) never terminate in binary — the converter truncates those at 32 bits and marks them approximate. That is the honest limit of any finite binary fraction, not a bug.

Signed Numbers and Two’s Complement

The same bits can be two different numbers — the bit width decides.

Unsigned, 11111111 is 255. In signed 8-bit two’s complement, the leading 1 marks a negative value and the same string is −1 (it reads as 255 − 256). Likewise 10000000 is 128 unsigned but −128 signed. Signed interpretation only exists at a fixed width — 8, 16, 32 or 64 bits — because the sign lives in the top bit. Enable Signed above and choose the width your data uses; unsigned mode handles any length.

More on number-versus-text readings of the same bits: binary numbers vs binary text. The broader story of why computers count in base 2: how binary numbers work.

Reference Tables

Powers of two for the place values, and every byte value in decimal, binary and hex.

Powers of two

Power	Value
2⁰	1
2¹	2
2²	4
2³	8
2⁴	16
2⁵	32
2⁶	64
2⁷	128
2⁸	256
2⁹	512
2¹⁰	1024
2¹¹	2048
2¹²	4096
2¹³	8192
2¹⁴	16384
2¹⁵	32768
2¹⁶	65536

Every byte value: 0–255 in decimal, binary and hex

Decimal	Binary	Hex
0	00000000	0x00
1	00000001	0x01
2	00000010	0x02
3	00000011	0x03
4	00000100	0x04
5	00000101	0x05
6	00000110	0x06
7	00000111	0x07
8	00001000	0x08
9	00001001	0x09
10	00001010	0x0A
11	00001011	0x0B
12	00001100	0x0C
13	00001101	0x0D
14	00001110	0x0E
15	00001111	0x0F
16	00010000	0x10
17	00010001	0x11
18	00010010	0x12
19	00010011	0x13
20	00010100	0x14
21	00010101	0x15
22	00010110	0x16
23	00010111	0x17
24	00011000	0x18
25	00011001	0x19
26	00011010	0x1A
27	00011011	0x1B
28	00011100	0x1C
29	00011101	0x1D
30	00011110	0x1E
31	00011111	0x1F
32	00100000	0x20
33	00100001	0x21
34	00100010	0x22
35	00100011	0x23
36	00100100	0x24
37	00100101	0x25
38	00100110	0x26
39	00100111	0x27
40	00101000	0x28
41	00101001	0x29
42	00101010	0x2A
43	00101011	0x2B
44	00101100	0x2C
45	00101101	0x2D
46	00101110	0x2E
47	00101111	0x2F
48	00110000	0x30
49	00110001	0x31
50	00110010	0x32
51	00110011	0x33
52	00110100	0x34
53	00110101	0x35
54	00110110	0x36
55	00110111	0x37
56	00111000	0x38
57	00111001	0x39
58	00111010	0x3A
59	00111011	0x3B
60	00111100	0x3C
61	00111101	0x3D
62	00111110	0x3E
63	00111111	0x3F
64	01000000	0x40
65	01000001	0x41
66	01000010	0x42
67	01000011	0x43
68	01000100	0x44
69	01000101	0x45
70	01000110	0x46
71	01000111	0x47
72	01001000	0x48
73	01001001	0x49
74	01001010	0x4A
75	01001011	0x4B
76	01001100	0x4C
77	01001101	0x4D
78	01001110	0x4E
79	01001111	0x4F
80	01010000	0x50
81	01010001	0x51
82	01010010	0x52
83	01010011	0x53
84	01010100	0x54
85	01010101	0x55
86	01010110	0x56
87	01010111	0x57
88	01011000	0x58
89	01011001	0x59
90	01011010	0x5A
91	01011011	0x5B
92	01011100	0x5C
93	01011101	0x5D
94	01011110	0x5E
95	01011111	0x5F
96	01100000	0x60
97	01100001	0x61
98	01100010	0x62
99	01100011	0x63
100	01100100	0x64
101	01100101	0x65
102	01100110	0x66
103	01100111	0x67
104	01101000	0x68
105	01101001	0x69
106	01101010	0x6A
107	01101011	0x6B
108	01101100	0x6C
109	01101101	0x6D
110	01101110	0x6E
111	01101111	0x6F
112	01110000	0x70
113	01110001	0x71
114	01110010	0x72
115	01110011	0x73
116	01110100	0x74
117	01110101	0x75
118	01110110	0x76
119	01110111	0x77
120	01111000	0x78
121	01111001	0x79
122	01111010	0x7A
123	01111011	0x7B
124	01111100	0x7C
125	01111101	0x7D
126	01111110	0x7E
127	01111111	0x7F
128	10000000	0x80
129	10000001	0x81
130	10000010	0x82
131	10000011	0x83
132	10000100	0x84
133	10000101	0x85
134	10000110	0x86
135	10000111	0x87
136	10001000	0x88
137	10001001	0x89
138	10001010	0x8A
139	10001011	0x8B
140	10001100	0x8C
141	10001101	0x8D
142	10001110	0x8E
143	10001111	0x8F
144	10010000	0x90
145	10010001	0x91
146	10010010	0x92
147	10010011	0x93
148	10010100	0x94
149	10010101	0x95
150	10010110	0x96
151	10010111	0x97
152	10011000	0x98
153	10011001	0x99
154	10011010	0x9A
155	10011011	0x9B
156	10011100	0x9C
157	10011101	0x9D
158	10011110	0x9E
159	10011111	0x9F
160	10100000	0xA0
161	10100001	0xA1
162	10100010	0xA2
163	10100011	0xA3
164	10100100	0xA4
165	10100101	0xA5
166	10100110	0xA6
167	10100111	0xA7
168	10101000	0xA8
169	10101001	0xA9
170	10101010	0xAA
171	10101011	0xAB
172	10101100	0xAC
173	10101101	0xAD
174	10101110	0xAE
175	10101111	0xAF
176	10110000	0xB0
177	10110001	0xB1
178	10110010	0xB2
179	10110011	0xB3
180	10110100	0xB4
181	10110101	0xB5
182	10110110	0xB6
183	10110111	0xB7
184	10111000	0xB8
185	10111001	0xB9
186	10111010	0xBA
187	10111011	0xBB
188	10111100	0xBC
189	10111101	0xBD
190	10111110	0xBE
191	10111111	0xBF
192	11000000	0xC0
193	11000001	0xC1
194	11000010	0xC2
195	11000011	0xC3
196	11000100	0xC4
197	11000101	0xC5
198	11000110	0xC6
199	11000111	0xC7
200	11001000	0xC8
201	11001001	0xC9
202	11001010	0xCA
203	11001011	0xCB
204	11001100	0xCC
205	11001101	0xCD
206	11001110	0xCE
207	11001111	0xCF
208	11010000	0xD0
209	11010001	0xD1
210	11010010	0xD2
211	11010011	0xD3
212	11010100	0xD4
213	11010101	0xD5
214	11010110	0xD6
215	11010111	0xD7
216	11011000	0xD8
217	11011001	0xD9
218	11011010	0xDA
219	11011011	0xDB
220	11011100	0xDC
221	11011101	0xDD
222	11011110	0xDE
223	11011111	0xDF
224	11100000	0xE0
225	11100001	0xE1
226	11100010	0xE2
227	11100011	0xE3
228	11100100	0xE4
229	11100101	0xE5
230	11100110	0xE6
231	11100111	0xE7
232	11101000	0xE8
233	11101001	0xE9
234	11101010	0xEA
235	11101011	0xEB
236	11101100	0xEC
237	11101101	0xED
238	11101110	0xEE
239	11101111	0xEF
240	11110000	0xF0
241	11110001	0xF1
242	11110010	0xF2
243	11110011	0xF3
244	11110100	0xF4
245	11110101	0xF5
246	11110110	0xF6
247	11110111	0xF7
248	11111000	0xF8
249	11111001	0xF9
250	11111010	0xFA
251	11111011	0xFB
252	11111100	0xFC
253	11111101	0xFD
254	11111110	0xFE
255	11111111	0xFF

Common Mistakes

Mistake: reading place values from the left. 1101 is not 1 + 2 + 4 + 8. Correction: the smallest value (1) is always the rightmost bit — count from the right.
Mistake: mixing up number and text. 01001000 is 72 as a number but the letter H as text. Correction: decide what the bits mean before converting — the note above the tool links the right converter.
Mistake: forgetting that signed needs a width. Correction: two’s complement only exists at a fixed bit width — 11111111 is −1 at 8 bits, 65535 unsigned. Pick the width before reading a signed value.

Practice

1. Convert 1101 to decimal. 8 + 4 + 1 = 13.

2. Write 42 in binary with double dabble. 42 → 21 → 10 → 5 → 2 → 1, remainders 0, 1, 0, 1, 0, 1 → read bottom to top: 101010.

3. What is 11111111 unsigned, and signed 8-bit? Unsigned: 255; signed 8-bit: −1. Verify both with the Signed toggle above.

Common Values, One Click

Each link opens this converter with the value pre-filled.

1010 in decimal (10) 1111 in decimal (15) 10100 in decimal (20) 1100100 in decimal (100) 11111111 in decimal (255) 10000000000 in decimal (1024)

Binary to Decimal FAQ

How do I convert binary to decimal?

Add the place values wherever you see a 1 — positions double from right to left (1, 2, 4, 8, 16…). For example 1010 is 8 + 2 = 10. The converter above does this instantly, for any length of input.

How do I convert a negative binary number?

It depends on the bit width. In signed 8-bit two’s complement, 11111111 is −1 and 10000000 is −128; unsigned, the same strings are 255 and 128. Enable Signed above and pick the width your data uses.

Can binary numbers have a decimal point?

Yes — a binary point. Digits after it are worth 1/2, 1/4, 1/8 and so on, so 101.11 is 5 + 1/2 + 1/4 = 5.75. This converter handles fractional binary in both directions.

Is there a biggest number this converter handles?

No practical limit: whole numbers are handled with arbitrary-length arithmetic, so a 100-bit or 1000-bit string converts exactly. One honest caveat: fractions that never terminate in binary are truncated to 32 bits and clearly marked as approximate.

What is the difference between a binary number and binary text?

A binary number is a value in base 2 — 01001000 means 72. Binary text is the same bits read as character codes — 01001000 means the letter H. If you want letters, use our binary to text converter; if you want the value, you are in the right place.

What do 0b and 0x prefixes mean?

0b marks a binary literal and 0x marks hexadecimal in programming languages. Both are notation, not part of the value — this converter accepts a 0b prefix and shows the hex spelling of every result.