Binary to decimal converter

Binary to decimal conversion table

A 1 followed by zeros is always a power of 2. 10 is 2, 100 is 4, 1000 is 8, and 100000000 is 256. A run of 1s is one less than the next power, so 1111 is 15 and 11111111 is 255.

Odd numbers always end in 1 and even numbers in 0, because every place value except the rightmost 1 is even. That makes the last bit a quick check on any result: 10101 ends in 1 and gives the odd number 21.

How to convert binary to decimal

Binary is base 2, with only the digits 0 and 1. Each place is worth twice the place to its right. From the right, the place values are 1, 2, 4, 8, 16, 32, 64 and 128 for the first eight bits.

Write those values over the bits, keep the ones above a 1 and add them. For 1100100 the 1 bits sit on 64, 32 and 4, and 64 + 32 + 4 = 100. For 10101 they sit on 16, 4 and 1, which gives 21.

The doubling method works from the left. Start at 0, and for each bit double the total and add the bit. For 1011 that runs 1, 2, 5, 11. The converter reads the digits this way with exact integers, so a string of hundreds of bits gives every decimal digit.

Converting a byte to decimal

A byte is 8 bits, so its value runs from 00000000, which is 0, to 11111111, which is 255. The leading zeros of a byte are allowed in the Number field: 00000001 gives 1, 01000001 gives 65 and 10000000 gives 128. Each byte therefore has 256 possible values.

The 65 of 01000001 is also the ASCII code of the capital letter A. This page returns the number only. It does not turn bytes into letters or read binary text.

Convert one byte at a time. A space between bytes is rejected, so 01000001 01000010 gives an error. If you join the two bytes into one 16-bit string, the converter reads them as a single number, and 0100000101000010 gives 16706. The largest 16-bit string, sixteen 1s, gives 65535, which is 2 to the power 16 minus 1.

Using the binary to decimal converter

The page opens with Binary (2) in From base and Decimal (10) in To base. Type or paste the bits in the Number field and select Convert number. The Converted number panel shows the decimal value, with Copy result and Download TXT beside it.

Only 0 and 1 are valid digits here. A 2 in 1102 is rejected as a digit that is not valid in the input base, and so is the b of a 0b1010 prefix. A binary point, as in 1010.1, is rejected because the converter takes whole numbers only.

The converter reads the bits as an unsigned number with an optional sign. It does not apply two's complement, so 11111011 gives 251, not −5. Swap bases turns the form into decimal to binary and moves the result into the Number field. Reset returns to binary to decimal.