binary to denary calculator - Aaron Graves, PhDude Replica

Instant Binary to Denary Converter

Enter a binary value (using only 0 and 1) and click calculate.

Binary Number

Tip: spaces and underscores are allowed (example: 1010 1101 or 1010_1101).

What is a binary to denary calculator?

A binary to denary calculator converts numbers from base-2 (binary) to base-10 (denary/decimal). In binary, each digit is called a bit and can only be 0 or 1. In denary, we use the familiar digits 0 through 9.

The calculator above does the conversion instantly and also shows the place-value breakdown, so you can see exactly how the answer is produced.

How conversion works

Binary place values

Each position in a binary number represents a power of 2, starting from the right:

Rightmost bit: 2^0 = 1
Next bit: 2^1 = 2
Then: 2^2 = 4, 2^3 = 8, 2^4 = 16, and so on

Manual method in 3 steps

Write down each bit with its power of 2.
Keep only the values where the bit is 1.
Add those values together to get the denary result.

Example: 10110
1×16 + 0×8 + 1×4 + 1×2 + 0×1 = 22
So, 10110₂ = 22₁₀.

Worked examples

Example 1: 1101

1×8 + 1×4 + 0×2 + 1×1 = 8 + 4 + 0 + 1 = 13
Result: 13

Example 2: 100000

1×32 + 0×16 + 0×8 + 0×4 + 0×2 + 0×1 = 32
Result: 32

Example 3: 11111111

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255
Result: 255

Common mistakes to avoid

Using digits other than 0 and 1.
Reading powers from left to right incorrectly.
Forgetting the rightmost bit is always 2^0.
Confusing denary (base-10) with hexadecimal (base-16).

Why binary to denary matters

Binary is the native language of digital electronics. Converting between binary and denary is foundational for:

Computer science and programming
Networking and subnetting
Digital systems and embedded devices
GCSE/A-Level and introductory university computing courses

Quick reference values

0001 = 1
0010 = 2
0100 = 4
1000 = 8
10000 = 16
100000 = 32
1000000 = 64
10000000 = 128

FAQ

Is denary the same as decimal?

Yes. “Denary” and “decimal” both mean base-10.

Can this calculator handle long binary numbers?

Yes. This page uses BigInt-based conversion logic, so very long binary strings can be converted reliably (limited only by browser memory/performance).

Can I type a number like 0b1010?

Yes. The calculator accepts optional 0b prefix and ignores spaces/underscores.