Binary to Decimal Converter

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Conversion Results

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Free Online Tool

Convert between binary, decimal, octal, hexadecimal, and text — instantly. With step-by-step breakdowns and 2's complement support.

5Number Systems
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Base 2

Binary System

Binary number is a number expressed in the base 2 numeral system. Binary number's digits have 2 symbols: zero (0) and one (1). Each digit of a binary number counts a power of 2.

The binary numeral system uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only 2 numbers: 0 and 1. The binary system has become the language of electronics and computers. This is the most efficient system to detect an electric signal's off (0) and on (1) state. It is the basis for binary code that composes data in computer-based machines.

Example 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀
Toggle Bits — Click Each Bit to See the Decimal Value Update
Binary: 00000000 = 0 ₁₀
0
Base 10

Decimal System

Enter a Decimal Number to See Each Digit's Positional Value

Decimal number is a number expressed in the base 10 numeral system. Decimal number's digits have 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit of a decimal number counts a power of 10.

The decimal numeral system is the most commonly used number system in daily life. It uses the number 10 as its base (radix). The Hindu-Arabic numeral system gives positions to the digits in a number, and this method works by using powers of the base 10. Digits are raised to the nth power, in accordance with their position.

Example 653₁₀ = 6×10² + 5×10¹ + 3×10⁰
Read

How to Read a Binary Number

Reading a binary number requires understanding positional notation. In the binary system, each binary digit (bit) is a power of 2. Every binary number is represented as powers of 2, with the rightmost bit in the position of 2⁰. Each bit refers to 1 bit of data.

Example The binary number (1010)₂ can be written as: (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)
Enter a Binary Number to See Position Labels
Convert

How to Convert Binary to Decimal

There are 2 methods to apply binary to decimal conversion. The first method uses positional representation of the binary number. The second method is called double dabble, used for converting longer binary strings faster.

1

Write down the binary number.

2

Starting with the least significant bit (LSB — the rightmost digit), multiply each digit by the value of the position. Continue to the most significant bit (MSB — the leftmost digit).

3

Add the results to get the decimal equivalent of the given binary number.

Step-Through: Positional Method
1

Start with 0. Double the total (0 × 2 = 0) and add the leftmost digit.

2

Double the total and add the next leftmost digit.

3

Repeat until all digits are processed. The final total is the decimal equivalent.

Double dabble is an algorithm that converts from any base to decimal. The rule: double the running total and add the next digit. Start from the leftmost digit with a total of 0.

Step-Through: Double Dabble Method

Binary to Decimal Conversion Examples

111001₂ = 57₁₀
1101₂ = 13₁₀
11011₂ = 27₁₀
Chart

Binary to Decimal Conversion Table

Complete binary to decimal conversion chart with hexadecimal (hex) and octal number equivalents for all 8-bit values.

Binary Decimal Hex Octal
00000000 0 0 0
00000001 1 1 1
00000010 2 2 2
00000011 3 3 3
00000100 4 4 4
00000101 5 5 5
00000110 6 6 6
00000111 7 7 7
00001000 8 8 10
00001001 9 9 11
00001010 10 A 12
00001011 11 B 13
00001100 12 C 14
00001101 13 D 15
00001110 14 E 16
00001111 15 F 17
00010000 16 10 20
00010001 17 11 21
00010010 18 12 22
00010011 19 13 23
00010100 20 14 24
00010101 21 15 25
00010110 22 16 26
00010111 23 17 27
00011000 24 18 30
00011001 25 19 31
00011010 26 1A 32
00011011 27 1B 33
00011100 28 1C 34
00011101 29 1D 35
00011110 30 1E 36
00011111 31 1F 37
00100000 32 20 40
00100001 33 21 41
00100010 34 22 42
00100011 35 23 43
00100100 36 24 44
00100101 37 25 45
00100110 38 26 46
00100111 39 27 47
00101000 40 28 50
00101001 41 29 51
00101010 42 2A 52
00101011 43 2B 53
00101100 44 2C 54
00101101 45 2D 55
00101110 46 2E 56
00101111 47 2F 57
00110000 48 30 60
00110001 49 31 61
00110010 50 32 62
00110011 51 33 63
00110100 52 34 64
00110101 53 35 65
00110110 54 36 66
00110111 55 37 67
00111000 56 38 70
00111001 57 39 71
00111010 58 3A 72
00111011 59 3B 73
00111100 60 3C 74
00111101 61 3D 75
00111110 62 3E 76
00111111 63 3F 77
01000000 64 40 100
01000001 65 41 101
01000010 66 42 102
01000011 67 43 103
01000100 68 44 104
01000101 69 45 105
01000110 70 46 106
01000111 71 47 107
01001000 72 48 110
01001001 73 49 111
01001010 74 4A 112
01001011 75 4B 113
01001100 76 4C 114
01001101 77 4D 115
01001110 78 4E 116
01001111 79 4F 117
01010000 80 50 120
01010001 81 51 121
01010010 82 52 122
01010011 83 53 123
01010100 84 54 124
01010101 85 55 125
01010110 86 56 126
01010111 87 57 127
01011000 88 58 130
01011001 89 59 131
01011010 90 5A 132
01011011 91 5B 133
01011100 92 5C 134
01011101 93 5D 135
01011110 94 5E 136
01011111 95 5F 137
01100000 96 60 140
01100001 97 61 141
01100010 98 62 142
01100011 99 63 143
01100100 100 64 144
01100101 101 65 145
01100110 102 66 146
01100111 103 67 147
01101000 104 68 150
01101001 105 69 151
01101010 106 6A 152
01101011 107 6B 153
01101100 108 6C 154
01101101 109 6D 155
01101110 110 6E 156
01101111 111 6F 157
01110000 112 70 160
01110001 113 71 161
01110010 114 72 162
01110011 115 73 163
01110100 116 74 164
01110101 117 75 165
01110110 118 76 166
01110111 119 77 167
01111000 120 78 170
01111001 121 79 171
01111010 122 7A 172
01111011 123 7B 173
01111100 124 7C 174
01111101 125 7D 175
01111110 126 7E 176
01111111 127 7F 177
10000000 128 80 200
10000001 129 81 201
10000010 130 82 202
10000011 131 83 203
10000100 132 84 204
10000101 133 85 205
10000110 134 86 206
10000111 135 87 207
10001000 136 88 210
10001001 137 89 211
10001010 138 8A 212
10001011 139 8B 213
10001100 140 8C 214
10001101 141 8D 215
10001110 142 8E 216
10001111 143 8F 217
10010000 144 90 220
10010001 145 91 221
10010010 146 92 222
10010011 147 93 223
10010100 148 94 224
10010101 149 95 225
10010110 150 96 226
10010111 151 97 227
10011000 152 98 230
10011001 153 99 231
10011010 154 9A 232
10011011 155 9B 233
10011100 156 9C 234
10011101 157 9D 235
10011110 158 9E 236
10011111 159 9F 237
10100000 160 A0 240
10100001 161 A1 241
10100010 162 A2 242
10100011 163 A3 243
10100100 164 A4 244
10100101 165 A5 245
10100110 166 A6 246
10100111 167 A7 247
10101000 168 A8 250
10101001 169 A9 251
10101010 170 AA 252
10101011 171 AB 253
10101100 172 AC 254
10101101 173 AD 255
10101110 174 AE 256
10101111 175 AF 257
10110000 176 B0 260
10110001 177 B1 261
10110010 178 B2 262
10110011 179 B3 263
10110100 180 B4 264
10110101 181 B5 265
10110110 182 B6 266
10110111 183 B7 267
10111000 184 B8 270
10111001 185 B9 271
10111010 186 BA 272
10111011 187 BB 273
10111100 188 BC 274
10111101 189 BD 275
10111110 190 BE 276
10111111 191 BF 277
11000000 192 C0 300
11000001 193 C1 301
11000010 194 C2 302
11000011 195 C3 303
11000100 196 C4 304
11000101 197 C5 305
11000110 198 C6 306
11000111 199 C7 307
11001000 200 C8 310
11001001 201 C9 311
11001010 202 CA 312
11001011 203 CB 313
11001100 204 CC 314
11001101 205 CD 315
11001110 206 CE 316
11001111 207 CF 317
11010000 208 D0 320
11010001 209 D1 321
11010010 210 D2 322
11010011 211 D3 323
11010100 212 D4 324
11010101 213 D5 325
11010110 214 D6 326
11010111 215 D7 327
11011000 216 D8 330
11011001 217 D9 331
11011010 218 DA 332
11011011 219 DB 333
11011100 220 DC 334
11011101 221 DD 335
11011110 222 DE 336
11011111 223 DF 337
11100000 224 E0 340
11100001 225 E1 341
11100010 226 E2 342
11100011 227 E3 343
11100100 228 E4 344
11100101 229 E5 345
11100110 230 E6 346
11100111 231 E7 347
11101000 232 E8 350
11101001 233 E9 351
11101010 234 EA 352
11101011 235 EB 353
11101100 236 EC 354
11101101 237 ED 355
11101110 238 EE 356
11101111 239 EF 357
11110000 240 F0 360
11110001 241 F1 361
11110010 242 F2 362
11110011 243 F3 363
11110100 244 F4 364
11110101 245 F5 365
11110110 246 F6 366
11110111 247 F7 367
11111000 248 F8 370
11111001 249 F9 371
11111010 250 FA 372
11111011 251 FB 373
11111100 252 FC 374
11111101 253 FD 375
11111110 254 FE 376
11111111 255 FF 377
Showing 256 of 256 entries
Basics

Binary System Basics

The binary numeral system is the foundation of all digital computing. Binary uses base 2, where each binary digit (bit) has a weighted value equal to a power of 2. There are 4 key size units in binary.

1 Bit

1 Bit — The smallest unit of data. Has 2 possible values: 0 or 1.

0 1

4 Bits (Nibble)

4 Bits (Nibble) — Represents a single hexadecimal digit. Can store 16 values (0–15).

0000 → 1111

8 Bits (Byte)

8 Bits (Byte) — The standard unit of data storage. Can store 256 values (0–255).

00000000 → 11111111

16+ Bits (Word)

16/32/64 Bits (Word) — Used by processors. A 32-bit word holds over 4 billion values.

16-bit 32-bit 64-bit
Powers of 2 Visualization
Formula

Binary to Decimal Conversion Formula & Rules

For a binary number with n digits: d(n-1) ... d₃ d₂ d₁ d₀, the decimal number equals the sum of binary digits (dₙ) times their power of 2 (2ⁿ).

decimal = d₀×2⁰ + d₁×2¹ + d₂×2² + ... + d(n-1)×2^(n-1)
1

Each binary digit is multiplied by its corresponding power of 2.

2

Powers of 2 increase from right (2⁰) to left (2ⁿ⁻¹).

3

A binary digit of 0 contributes nothing to the decimal sum.

4

A binary digit of 1 adds the full power of 2 for that position.

Enter a Binary Number to See the Formula in Action
Examples

Worked Binary to Decimal Examples

111001₂ = 57₁₀
2⁵ 1 32
2⁴ 1 16
2³ 1 8
2² 0 0
2¹ 0 0
2⁰ 1 1
32 + 16 + 8 + 1 = 57
1101₂ = 13₁₀
2³ 1 8
2² 1 4
2¹ 0 0
2⁰ 1 1
8 + 4 + 1 = 13
11011₂ = 27₁₀
2⁴ 1 16
2³ 1 8
2² 0 0
2¹ 1 2
2⁰ 1 1
16 + 8 + 2 + 1 = 27
10101₂ = 21₁₀
2⁴ 1 16
2³ 0 0
2² 1 4
2¹ 0 0
2⁰ 1 1
16 + 4 + 1 = 21
1110010₂ = 114₁₀
2⁶ 1 64
2⁵ 1 32
2⁴ 1 16
2³ 0 0
2² 0 0
2¹ 1 2
2⁰ 0 0
64 + 32 + 16 + 2 = 114
10000000₂ = 128₁₀
2⁷ 1 128
2⁶ 0 0
2⁵ 0 0
2⁴ 0 0
2³ 0 0
2² 0 0
2¹ 0 0
2⁰ 0 0
128 = 128
Sizes

Binary Fractions & Bit Sizes

Binary numbers can have decimals. Binary fractions use a radix point (the binary equivalent of a decimal point) to represent values between integers. For the integer part, powers of 2 go up (2⁰, 2¹, 2²...). For the fractional part, powers of 2 go down (2⁻¹ = 0.5, 2⁻² = 0.25...).

8-bit 256 values
Unsigned 0 to 255
Signed -128 to 127
16-bit 65,536 values
Unsigned 0 to 65,535
Signed -32,768 to 32,767
32-bit 4,294,967,296 values
Unsigned 0 to 4,294,967,295
Signed -2,147,483,648 to 2,147,483,647
64-bit 1.8×10¹⁹ values
Unsigned 0 to 18,446,744,073,709,551,615
Signed -9.2×10¹⁸ to 9.2×10¹⁸
Binary Fraction Example: Radix Point
Integer Part
2² 1 4
2¹ 1 2
2⁰ 1 1
. Radix Point
Fractional Part
2⁻¹ 0 0
2⁻² 1 0.25
2⁻³ 0 0
2⁻⁴ 1 0.0625
111.0101₂ = 4 + 2 + 1 + 0.25 + 0.0625 = 7.3125₁₀
More

Other Number System Conversions

Related numeral systems converters for number conversion between binary, decimal, hexadecimal, octal, and ASCII text.

01.1→10 Binary Fraction to Decimal ±01→10 Signed Binary to Decimal 01→FF Binary to Hexadecimal 01→07 Binary to Octal N→N Binary Base Converter 01+01 Binary Calculator 01+01 Binary Addition 01−01 Binary Subtraction → 1,2,3 Step-by-Step Solver 0…255 Binary Table Generator 01→A Binary to Text A→01 Text to Binary ±1.M×2ᴱ Floating Point Converter 8b→256 Bit Size Converter & | ^ ~ Bitwise Operations 01→? Binary Decoder
FAQ

Frequently Asked Questions

What is binary to decimal conversion?
Binary to decimal conversion is the process of translating a binary number (base 2 numeral system) into a decimal number (base 10 numeral system). Each binary digit is multiplied by its corresponding power of 2, and the results are summed to produce the decimal equivalent. For example, 1101₂ = 1×8 + 1×4 + 0×2 + 1×1 = 13₁₀.
Why do we convert binary to decimal?
Binary to decimal conversion is necessary because computers process data in binary (base 2) while humans read numbers in decimal (base 10). Converting binary to decimal makes computer output readable for people. Programmers, engineers, and students convert binary to decimal when debugging code, analyzing network protocols, or studying computer science.
Why use binary instead of decimal?
Binary is used instead of decimal in computers because electronic circuits operate in 2 states: on (1) and off (0). The base 2 numeral system maps directly to these electrical states. Binary is more reliable for digital electronics because distinguishing between 2 voltage levels is simpler and less error-prone than distinguishing between 10 levels.
Why is binary better than decimal?
Binary is better than decimal for digital computing because it matches the physical design of electronic hardware. Transistors work as switches with 2 states (on/off), making binary the natural number system for processors. Binary also simplifies arithmetic operations at the hardware level — addition, subtraction, and multiplication are faster in base 2.
Can binary numbers have decimals?
Yes, binary numbers can have decimals. A binary fraction uses a radix point (the binary version of a decimal point) to separate the integer part from the fractional part. The fractional binary digits represent negative powers of 2: the first digit after the radix point is 2⁻¹ (0.5), the second is 2⁻² (0.25), and so on. For example, 111.0101₂ = 7.3125₁₀.
Are binary numbers base 2?
Yes, binary numbers are base 2. The binary numeral system uses exactly 2 digits — zero (0) and one (1). Each position in a binary number represents a power of 2, starting from 2⁰ on the right. This is why binary is called the base 2 numeral system.
Are binary numbers integers?
No, binary numbers are not limited to integers. Binary can represent both integers and fractional values. Integer binary numbers contain only whole-number positions (2⁰, 2¹, 2², etc.). Binary fractions use a radix point followed by negative powers of 2 (2⁻¹, 2⁻², etc.) to represent non-integer values.
Is binary a decimal system?
No, binary is not a decimal system. Binary is a base 2 numeral system with 2 digits (0 and 1). Decimal is a base 10 numeral system with 10 digits (0 through 9). These are 2 distinct numeral systems with different bases, though values in one system can be converted to the other.
When counting in binary, what comes after 0?
When counting in binary, 1 comes after 0. The binary numeral system has only 2 symbols: zero (0) and one (1). Binary counting proceeds: 0, 1, 10, 11, 100, 101, 110, 111, 1000. Each time all digits reach 1, a new digit is added on the left (similar to how decimal advances from 9 to 10).
When counting in binary, what comes after 1?
When counting in binary, 10 comes after 1. Since binary has only 2 digits (0 and 1), after 1 there is no single digit left, so a carry occurs. The 1 carries to the next position, producing 10₂ (which equals 2₁₀ in decimal). This follows the same carry principle that decimal uses when going from 9 to 10.
Which binary number is equivalent to decimal 5?
The binary number 101 is equivalent to decimal 5. The conversion: 1×2² + 0×2¹ + 1×2⁰ = 4 + 0 + 1 = 5₁₀. In binary, decimal 5 requires 3 bits to represent.
Which binary number is equivalent to decimal 9?
The binary number 1001 is equivalent to decimal 9. The conversion: 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 8 + 0 + 0 + 1 = 9₁₀. In binary, decimal 9 requires 4 bits to represent.
How do I convert binary to decimal?
To convert binary to decimal, multiply each binary digit by its corresponding power of 2 (starting from 2⁰ on the right), then sum all the values. For example: 1011₂ = (1×8) + (0×4) + (1×2) + (1×1) = 11₁₀. This is the positional method. A second method, double dabble, works by doubling the running total and adding the next digit from left to right.
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