Binary to Decimal Converter

Binary (base 2) is how computers store every number: each digit, or bit, is either 0 or 1. Reading a binary number as decimal is a matter of adding up powers of 2, and this converter shows exactly which ones. It also gives the hex and octal forms, which are shorter ways to write the same bits.

How to use the binary to decimal converter

1. Type or paste the binary number. A 0b prefix is optional, and spaces and underscores are ignored, so 1100 1000 and 0b1100_1000 both work.
2. Leave Convert from set to binary. You can switch it to octal, decimal or hex at any time.
3. Read the decimal result, along with the octal and hex forms.
4. Check the working under the result: each bit times its power of 2, added up.
5. Use the copy button next to any result to copy it.

How it works

In binary, each position is worth twice the position to its right. The rightmost bit is worth 2⁰ = 1, the next 2¹ = 2, then 4, 8, 16 and so on. Multiply each bit by its place value and add:

decimal = bₙ × 2ⁿ + … + b₂ × 2² + b₁ × 2¹ + b₀ × 2⁰

Because each bit is 0 or 1, that boils down to: add the place values of the 1 bits and ignore the 0 bits.

Bit position	7	6	5	4	3	2	1	0
Place value	128	64	32	16	8	4	2	1

Those eight positions make one byte. The converter works with whole numbers of any length using JavaScript’s BigInt; a regular JavaScript number is exact only up to 2⁵³ − 1, which a 54-bit binary number already exceeds.

Worked examples

1011 → 11

1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 8 + 2 + 1 = 11.

11001000 → 200

The 1 bits sit at positions 7, 6 and 3: 128 + 64 + 8 = 200. In hex that’s C8: the left four bits (1100) are C and the right four (1000) are 8.

11111111 → 255

All eight bits are 1: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. A shortcut: a run of n ones is always 2ⁿ − 1, here 2⁸ − 1 = 256 − 1.

10000000000 → 1,024

A 1 followed by ten zeros is 2¹⁰ = 1,024, the “kibi” in kibibyte (KiB).

Why hex is easier to read than binary

Every group of four bits is exactly one hex digit, so long binary numbers are often written in hex instead:

Binary	Hex	Decimal
0000	0	0
0101	5	5
1001	9	9
1010	A	10
1100	C	12
1111	F	15

So 1010 1010 is AA in hex and 170 in decimal (128 + 32 + 8 + 2).

Related guides

• Going the other way? The decimal to binary converter shows the repeated division by 2 and can pad to 8, 16, 32 or 64 bits.
• Converting hex instead? Use the hex to decimal converter.
• Bytes, kilobytes and kibibytes are all built on powers of 2 and 10: see the bytes to GB converter.