How to convert binary to decimal by hand
Example 1: 10011100 in binary is 156 in decimal
Binary to decimal: add up the place values
Each binary digit is worth its value times 2 raised to the power of its position, counting from 0 on the right.
| Digit | Place value | Digit × place value |
|---|---|---|
| 1 | 2⁷ = 128 | 1 × 128 = 128 |
| 0 | 2⁶ = 64 | 0 × 64 = 0 |
| 0 | 2⁵ = 32 | 0 × 32 = 0 |
| 1 | 2⁴ = 16 | 1 × 16 = 16 |
| 1 | 2³ = 8 | 1 × 8 = 8 |
| 1 | 2² = 4 | 1 × 4 = 4 |
| 0 | 2¹ = 2 | 0 × 2 = 0 |
| 0 | 2⁰ = 1 | 0 × 1 = 0 |
128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156
Example 2: 11000000 in binary is 192 in decimal
Binary to decimal: add up the place values
Each binary digit is worth its value times 2 raised to the power of its position, counting from 0 on the right.
| Digit | Place value | Digit × place value |
|---|---|---|
| 1 | 2⁷ = 128 | 1 × 128 = 128 |
| 1 | 2⁶ = 64 | 1 × 64 = 64 |
| 0 | 2⁵ = 32 | 0 × 32 = 0 |
| 0 | 2⁴ = 16 | 0 × 16 = 0 |
| 0 | 2³ = 8 | 0 × 8 = 0 |
| 0 | 2² = 4 | 0 × 4 = 0 |
| 0 | 2¹ = 2 | 0 × 2 = 0 |
| 0 | 2⁰ = 1 | 0 × 1 = 0 |
128 + 64 + 0 + 0 + 0 + 0 + 0 + 0 = 192
Binary to Decimal conversion table
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
| 10000 | 16 |
| 100000 | 32 |
| 1000000 | 64 |
| 1100100 | 100 |
| 10000000 | 128 |
| 11111111 | 255 |
| 100000000 | 256 |
| 1000000000 | 512 |
| 1111101000 | 1000 |
| 10000000000 | 1024 |
Where this conversion comes up
- Reading IPv4 addresses and masks written in binary: 11000000 is 192.
- Checking a register, status byte or bit field from a datasheet or debugger.
- Coursework, where you add up the powers of 2 for each 1 bit.
Frequently asked questions
Is there a quick way to convert binary to decimal in my head?
Write the place values 128, 64, 32, 16, 8, 4, 2, 1 above an 8-bit number and add the ones where the bit is 1. For 10011100 that is 128 + 16 + 8 + 4 = 156.
Does this handle signed (two's complement) binary?
No. The bits are read as an unsigned number. If your value is two's complement and the top bit is 1, subtract 2ⁿ (where n is the number of bits) from the result to get the signed value.
Can I convert negative numbers?
Yes. Put a minus sign in front and it is kept in the result, for example -10011100 becomes -156. The converter does not produce two's complement.
Is there a limit on how big the number can be?
No practical limit. The conversion uses arbitrary precision integers, so long values stay exact. The step-by-step working is shown for numbers up to 24 digits.
Can I convert fractions?
Not with this tool. It converts whole binary numbers to whole decimal numbers.
Other number converters
Going the other way? Use the Decimal to Binary Converter. To see a number in every base at once, try the all-in-one number converter.