Convert binary (base 2) numbers into decimal (base 10), including binary fractions and negatives, with place-value working.
To convert binary to decimal, multiply each binary digit by its matching power of 2 and add the results, starting with 2⁰ on the right. For example, 1010₂ equals 1×8 + 0×4 + 1×2 + 0×1 = 10₁₀. Digits after a binary point use negative powers of 2, so 0.101₂ = 0.5 + 0.125 = 0.625₁₀. This calculator shows every place-value step.
Digits 0 and 1 only. A binary point, a leading minus, the 0b prefix and spaces between groups are all fine.
Type a binary number — a whole value like 11001, a binary fraction like 1010.1, or a negative like -10010 — and press Convert. You may include spaces between groups of bits, a leading 0b prefix, and leading zeros; they do not change the value. The result shows the exact decimal, the expanded place-value working, and the totals. Use Copy result to reuse it. Negative values use a leading minus sign for readability; this is not the same as a fixed-width two's-complement pattern.
Each b is a binary digit (0 or 1) and each exponent is the position of that digit. Positions left of the point count up from 0; positions right of the point count down using negative powers, which are the fractions 0.5, 0.25, 0.125 and so on. Multiply, then add.
Binary is a positional number system, just like decimal, but each position is worth a power of 2 instead of a power of 10. In the number 1010, the leftmost 1 sits in the 8s place, the 0 in the 4s place, the next 1 in the 2s place, and the last 0 in the 1s place. Only the 8 and the 2 are switched on, so the value is 8 + 2 = 10.
Write the place values under each digit from right to left (1, 2, 4, 8, …). Multiply each digit by its place value, then add the products. For 11001: 16 + 8 + 0 + 0 + 1 = 25.
For digits after the point, use 0.5, 0.25, 0.125, 0.0625 and so on. For 0.101: the first digit is 1 (0.5), the second is 0, the third is 1 (0.125), giving 0.5 + 0.125 = 0.625. Because these place values have denominators that are powers of two, every finite binary fraction converts to a terminating decimal.
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 1000 | 8 |
| 1010 | 10 |
| 1111 | 15 |
| 10000 | 16 |
| 11111 | 31 |
| 100000 | 32 |
| 111111 | 63 |
| 1000000 | 64 |
| 1100100 | 100 |
| 1111111 | 127 |
| 10000000 | 128 |
| 11111111 | 255 |
| 100000000 | 256 |
| 1000000000 | 512 |
| 10000000000 | 1024 |
| Binary | Decimal |
|---|---|
| 0.1 | 0.5 |
| 0.01 | 0.25 |
| 0.11 | 0.75 |
| 0.001 | 0.125 |
| 0.101 | 0.625 |
| 0.111 | 0.875 |
| 1.1 | 1.5 |
| 10.01 | 2.25 |
| 1010.1 | 10.5 |
| Feature | Binary (base 2) | Decimal (base 10) |
|---|---|---|
| Digits used | 0 and 1 | 0–9 |
| Place values | 1, 2, 4, 8, 16… | 1, 10, 100, 1000… |
| Point name | Binary point | Decimal point |
| Example | 1010 | 10 |
A single binary digit is a bit. Four bits form a nibble, and eight bits form a byte. One byte holds 256 different patterns, from 00000000 (0) to 11111111 (255), which is why an 8-bit value tops out at 255. Larger values simply use more bits.
Reading binary as decimal comes up across computing: in programming and debugging, networking with IP addresses and subnet masks, digital logic and electronics, embedded systems and microcontrollers, computer memory and data representation, and in computer-science classes and coding interviews. It is the everyday bridge between how machines store numbers and how people read them.
1) 6 2) 9 3) 12 4) 21 5) 32
1) 200 2) 10.5 3) 0.875 4) 2.25 5) -42
How do you convert binary to decimal?
Multiply each binary digit by its matching power of 2 — starting at 2⁰ on the right — and add the results. For example, 1010 is 1×8 + 0×4 + 1×2 + 0×1 = 10.
What is 1010 in decimal?
1010 in binary is 10 in decimal, because it is 8 + 2.
What is 11001 in decimal?
11001 in binary is 25 in decimal, made of 16 + 8 + 1.
What is 11111111 in decimal?
11111111 in binary is 255 in decimal. It is the largest unsigned value that fits in one byte of 8 bits.
What is 10000000 in decimal?
10000000 in binary is 128 in decimal, because the single 1 sits in the 2⁷ (128) place.
How do binary place values work?
Each position is a power of two. From the right they are 1, 2, 4, 8, 16 and so on. You add the place values wherever there is a 1.
How do you convert a binary fraction to decimal?
Digits after the binary point use negative powers of two: 0.5, 0.25, 0.125, 0.0625. Multiply each digit by its place value and add. So 0.101 is 0.5 + 0.125 = 0.625.
What is 0.101 in decimal?
0.101 in binary is 0.625 in decimal, because it is 0.5 + 0.125.
What is 1010.1 in decimal?
1010.1 in binary is 10.5 in decimal: the whole part 1010 is 10, and the .1 adds 0.5.
Can binary numbers contain a point?
Yes. A binary point works like a decimal point, separating whole values from fractional ones. The digits after it use negative powers of two.
Do leading zeros change a binary number?
No. Leading zeros do not change the value, so 00001010 and 1010 are both 10. Zeros only matter as placeholders between other digits.
How do you convert negative binary to decimal?
Convert the digits after the minus sign as usual, then make the result negative. For example, -10010 is -(16 + 2) = -18.
What is the difference between signed binary and two's complement?
Signed-magnitude notation just puts a minus sign in front of the value, which is easy to read. Two's complement is a fixed-width method computers use to store negatives so that addition works cleanly. This calculator uses the readable minus-sign form.
What are bits, nibbles and bytes?
A bit is one binary digit. Four bits make a nibble, and eight bits make a byte, which can store 256 different values from 0 to 255.
Is this Binary to Decimal Calculator free?
Yes. It is free with no sign-up, works on any device, and runs in your browser so your entries stay private.