Binary to Decimal
FREEConvert binary to decimal and see how the answer was reached. Enter your binary number, using only 0s and 1s, and the converter shows the decimal value with a step-by-step breakdown. It also handles fractional binary, and it flags any digit that is not 0 or 1. It is free to use.
How to Convert Binary to Decimal
Binary is base 2: every digit is a 0 or a 1, and each position is worth twice the one to its right. To convert by hand, multiply each digit by its place value and add the results.
1. Write the place values under the digits, starting at 1 on the far right and doubling as you move left: 1, 2, 4, 8, 16, 32, 64, 128.
2. Multiply each digit by the place value under it. A 0 contributes nothing and a 1 contributes the whole place value.
3. Add the results.
Take 1001. From the left, the digits sit over 8, 4, 2 and 1, so the value is 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 9.
To skip the arithmetic, enter the number in the converter. It shows the same working for you.
Binary to Decimal Examples
Short binary numbers come up constantly, including 100, 101 and 1001:
| Binary | Working | Decimal |
| 100 | 1 × 4 + 0 × 2 + 0 × 1 | 4 |
| 101 | 1 × 4 + 0 × 2 + 1 × 1 | 5 |
| 1001 | 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 | 9 |
| 1101 | 8 + 4 + 0 + 1 | 13 |
| 10101 | 16 + 0 + 4 + 0 + 1 | 21 |
| 11111111 | 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 | 255 |
11111111 is the largest value that fits in 8 bits, which is why 255 turns up so often in computing.
Fractional Binary
A binary point works like a decimal point. Digits to its right are worth one half, one quarter, one eighth, and so on (the negative powers of 2). For 10101.011, the whole part is 16 + 4 + 1 = 21 and the fraction is 0.25 + 0.125 = 0.375, so the result is 21.375.
32-Bit Binary to Decimal
A 32-bit binary number has 32 digits. The method is unchanged: each digit is worth twice the one to its right, and the leftmost place is worth 2³¹, which is 2,147,483,648. If every digit is a 1, the unsigned value is 4,294,967,295, the largest number 32 bits can hold. To convert one, enter all 32 digits without spaces.
Here is a familiar one. The IPv4 address 192.168.1.1 is four 8-bit groups:
| Octet | Binary | Decimal |
| First | 11000000 | 192 |
| Second | 10101000 | 168 |
| Third | 00000001 | 1 |
| Fourth | 00000001 | 1 |
Joined into one 32-bit number, 11000000101010000000000100000001 is 3,232,235,777 in decimal.
Signed numbers. This converter reads binary as an unsigned number. In a signed 32-bit (two’s complement) system, a number that starts with 1 is negative. For example, all 32 ones means −1, not 4,294,967,295. To convert one by hand, take the unsigned value and subtract 2³² (4,294,967,296) when the leftmost bit is 1.
Binary vs BCD: What About Converting 10 to BCD?
BCD, or binary-coded decimal, is a different way of writing numbers. Instead of converting the whole number to binary, it writes each decimal digit as its own 4-bit group. The decimal number 10 has the digits 1 and 0, so in BCD it is 0001 0000. In ordinary binary, 10 is 1010.
The two are easy to confuse. Read 0001 0000 as ordinary binary and you get 16, not 10. This tool converts ordinary binary to decimal. It does not produce or read BCD.
Why Convert Binary to Decimal?
Computer internals: values stored in memory and registers are binary, but people read them in decimal.
IP addressing and subnetting: each part of an IPv4 address is an 8-bit binary number.
Debugging bitwise code: checking flags and masks means moving between binary and decimal.
Study and homework: checking your own working against the step-by-step breakdown.
Common Mistakes to Avoid
❌ Mistakes to Avoid
✓ Solution:
Counting positions from the wrong end. The rightmost digit is worth 1, and values double as you move left. Counting from the left gives the wrong answer.
Typing digits other than 0 and 1. Binary has only two digits. The converter flags a 2 through 9 as invalid.
Leaving out the binary point on a fraction. Digits after the point use negative powers of 2. Without the point, 10101011 and 10101.011 are very different numbers.
Making arithmetic slips with powers of 2. Mistakes usually happen in the larger place values, such as 2,048 or 2³¹. Compare your hand result against the breakdown.
Treating binary as signed. The same bits mean different things as unsigned and as two’s complement. This tool reads them as unsigned.
Frequently Asked Questions
Multiply each digit by 2 raised to its position, counting from 0 at the right, then add the results. For 1101, that is 8 + 4 + 0 + 1 = 13.
100 in binary is 4, 101 is 5, and 1001 is 9.
Enter all 32 digits. Each place is worth twice the one to its right, up to 2,147,483,648 for the leftmost digit, and the digits you set to 1 are added together. The largest unsigned result is 4,294,967,295.
No. It reads binary as unsigned. For a signed (two’s complement) number whose leftmost bit is 1, work out the unsigned value and subtract 2 raised to the number of bits.
Yes. Use a binary point. For example, 10101.011 is 21.375.
The converter flags digits other than 0 and 1 as invalid input.
Write each decimal digit as a 4-bit group: 1 is 0001 and 0 is 0000, so 10 is 0001 0000 in BCD. This tool converts ordinary binary to decimal and does not produce BCD.
Yes. It is free to use.
Convert Binary to Decimal
Enter your binary number and check the decimal value and the working. Use it to confirm your own calculations too.
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