Six bits: 101010
Binary
101010
Decimal
42
32 + 8 + 2 = 42. The 0s add nothing; they only hold their places.
Binary to Decimal Converter
Type a binary number and read its decimal value, with the working shown underneath. It opens on 101010, which is 42.
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How to convert binary to decimal
Binary is base 2, so it has two digits, 0 and 1, and each position is worth twice the one to its right: 1, 2, 4, 8, 16, 32, 64, 128 and so on. A binary number is a list of which of those place values are switched on.
That turns the conversion into an addition. Write the place values under the bits, keep the ones that sit under a 1 and add them. 1101 has 1s under 8, 4 and 1, so it is 13. The panel under the converter does this for whatever you type.
Spaces and a 0b prefix are ignored, and the arithmetic uses BigInt, so a 64-bit number converts without rounding.
What to know about binary numbers
- Place values double from right to left: 1, 2, 4, 8, 16, 32, 64, 128.
- Eight bits make a byte, which holds 0 to 255.
- A binary number that ends in 0 is even, and one that ends in 1 is odd.
- 4 bits count up to 15, 8 bits up to 255 and 16 bits up to 65535.
Binary to decimal, worked out
A full byte
Binary
11111111
Decimal
255
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255, the largest value one byte holds.
A file permission
Binary
111101101
Decimal
493
256 + 128 + 64 + 32 + 8 + 4 + 1 = 493, which is 755 in octal: the chmod 755 permission.
A power of two
Binary
10000000000
Decimal
1024
A single 1 followed by ten 0s is 2¹⁰, which is 1024.
Common binary to decimal mistakes
- Starting the powers at 1 instead of 0. The rightmost bit is worth 2⁰, which is 1.
- Reading the number from the wrong end. The leftmost bit carries the biggest value.
- Adding the place values under the 0s too. Only positions that hold a 1 count.
- Dropping leading zeros from a fixed-width value.
00001010and1010are both 10, but a byte field needs all eight bits.
Binary to decimal FAQ
What is 1010 in decimal?
10. The 1s sit on the 8 and the 2, and 8 + 2 = 10.
What is 11111111 in decimal?
255. Eight 1s switch on every place value from 1 to 128: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
How do I convert binary to decimal in Python?
Use
int('101010', 2), which returns 42. In JavaScript, parseInt('101010', 2) does the same.Is this the same as a binary translator?
No. This converts a binary number into its value. A binary translator turns text into the binary codes of its characters; for that, use the text to binary translator.
