Two's Complement Calculator – Signed Binary
Calculate two's complement representation for signed binary integers.
About This Calculator
Calculate two's complement representation for signed binary integers. Use the calculator above for instant results.
Worked Examples
- Invert 13 (00001101) → 11110010 + 1 = 11110011 = 0xF3
Answer: 11110011 (0xF3)
- = 11111111 = 0xFF
Answer: 11111111
- = 10000000 | Most negative 8-bit value
Answer: 10000000
Who Uses This Calculator?
Understand signed integer representation.
Signed number handling in hardware.
Demo two's complement system.
Debug signed integer issues.
Common Mistakes to Avoid
❌ Two's complement vs sign-magnitude
Two's complement (used by all modern CPUs) lets you add signed numbers the same way as unsigned. Sign-magnitude (not used) would need different adder circuits.
❌ MSB is the sign bit
In two's complement, the most significant bit is the sign: 0 = positive, 1 = negative.
Frequently Asked Questions
Why two's complement?
Single representation of zero. Addition works the same for signed and unsigned. No special hardware needed for subtraction.
How to find two's complement?
Method 1: Invert all bits (one's complement) then add 1. Method 2: Keep rightmost 1 and all bits to its right; invert everything to its left.
Range of n-bit signed integer?
From -2^(n-1) to 2^(n-1)-1. 8-bit: -128 to 127. 16-bit: -32768 to 32767. 32-bit: -2,147,483,648 to 2,147,483,647.