Binary to Decimal Converter

Start with 0. For each bit, double what you have and add the bit. Here is 11010110, which the converter returns as 214:

This works for any length and never needs a table of powers of two. To check the answer the other way, add the place values under each 1: 128 + 64 + 16 + 4 + 2 = 214.

• IP addresses and subnet masks. Each octet is 8 bits. 11000000 is 192 and 11111111 is 255, so a mask written as 24 ones and 8 zeros is 255.255.255.0.
• File permissions. The bits 111101101 are 493 in decimal, but the octal box in the panel shows 755, the form you would type into chmod.
• Bit flags and coursework. A settings value stored as bits is easier to compare once you have its decimal value.

Spaces are fine, so you can group bits for readability: 1101 0110 gives 214. Other characters cause problems, and the converter does not always warn you:

• A 0b prefix. 0b101 returns 0, because reading stops at the b. Type just 101 (5).
• A digit other than 0 or 1. Reading stops there. 1021 returns 2, the value of the 10 before the 2.
• A binary point. Fractions are dropped. 1010.11 returns 10, although the full value is 10.75.

The page opens with 42 in the box. That isn't a binary number, so you'll see an error message until you replace it with your own value.

Bits are always read as an unsigned number, so 11111111 is 255, not −1. If your 8 bits are a signed byte in two's complement and the leftmost bit is 1, subtract 256: 11111011 is 251, and 251 − 256 = −5. For 16 bits subtract 65536, and for 32 bits subtract 4294967296. A leading minus sign is kept as a plain sign, so -101 gives −5.

Answers are exact up to 53 bits (53 ones is 9007199254740991). Beyond that the result is rounded: a 1 followed by 52 zeros and a final 1 shows as 9007199254740992, one less than the true value.