Binary to Decimal Calculator – Base 2 to Base 10
Convert binary (base 2) numbers to decimal (base 10) and other bases.
About This Calculator
Convert binary (base 2) numbers to decimal (base 10) and other bases. Use the calculator above for instant results.
Worked Examples
- 1×8 + 1×4 + 0×2 + 1×1 = 13
Answer: 13
- = 255 (max 8-bit value = 0xFF)
Answer: 255
- = 128 (MSB set in 8-bit byte)
Answer: 128
Who Uses This Calculator?
Binary to decimal conversion.
Understand bit patterns.
Digital electronics.
Demo base conversion.
Common Mistakes to Avoid
❌ Leading zeros
1000 and 001000 are the same value (8). Leading zeros don't change the decimal value.
❌ Largest n-bit value
Maximum value of n-bit unsigned integer = 2^n - 1. 8-bit max = 255. 16-bit max = 65,535.
Frequently Asked Questions
Binary to decimal formula?
Each bit × its place value (power of 2). 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.
Decimal to binary?
Divide by 2 repeatedly, collect remainders from bottom up. Or use the math/binary-converter calculator.
Why binary in computers?
Electronic circuits have two states (on/off = 1/0). Binary maps perfectly to transistor states.