Two's complement calculator
Convert a signed decimal to its two's complement bit pattern, or paste bits to read them as a signed number. Pick the width your language or CPU uses.
Hex 0xFB · unsigned 251
What each bit is worth
1-128
164
132
116
18
04
12
11
The leftmost (sign) bit carries a negative weight. Add up the weights of the 1s to get -5.
Flip the bits, add one
- 1. Write 5 in 8 bits0000 0101
- 2. Invert every bit1111 1010
- 3. Add 11111 1011
Why flip-and-add-one works
For an N-bit number, flipping every bit of x gives (2N − 1) − x. Adding 1 makes it 2N − x, and because N-bit arithmetic wraps around at 2N, that value behaves exactly like −x. Add it to x and every bit carries out the top, leaving zero.
This is also why integer overflow wraps: in 8-bit, 127 + 1 = 10000000, which is −128. Try typing 127 and −128 above and compare the patterns. For unsigned conversions, use the decimal to binary converter; for AND/OR/NOT on these patterns, the bitwise calculator.
Questions people ask
What is two's complement?
Two's complement is how almost every computer stores signed integers. The leftmost bit has a negative weight (−128 in an 8-bit byte), and the other bits keep their normal positive weights. −5 in 8 bits is 11111011: −128 + 64 + 32 + 16 + 8 + 2 + 1 = −5.
How do I find the two's complement of a number?
Write the positive value in binary at the chosen width, flip every bit (0↔1), then add 1. For −5: 00000101 → 11111010 → 11111011.
What range can N bits hold?
From −2N−1 to 2N−1 − 1. 8 bits: −128 to 127. 16 bits: −32,768 to 32,767. 32 bits: −2,147,483,648 to 2,147,483,647.
Why do computers use two's complement instead of a sign bit?
Addition works the same for positive and negative numbers, so the CPU needs only one adder, and there is only one zero. Sign-magnitude and ones’ complement both have a +0 and −0.
How do I read a binary number as signed?
If the leftmost bit is 0, read it normally. If it is 1, subtract 2N from its unsigned value. 11111011 unsigned is 251; 251 − 256 = −5.