Signed Number Formats - How Computers Represent Negative Numbers

Two's Complement (the standard)

+5  = 0000 0101
invert → 1111 1010
add +1 → 1111 1011   (this is –5)

most significant bit (MSB) = sign bit (0 = positive, 1 = negative)

Why its GOOOOOOOD:

• Only one representation of zero: 0000 0000
• Addition and subtraction are the same for signed and unsigned numbers
• Simplifies hardware design

One's Complement (old, mostly obsolete, avoid)

+5  = 0000 0101
invert → 1111 1010   (this is –5 in one's complement)

Problem:

• Two representations of zero: +0 = 0000 0000 –0 = 1111 1111
• Addition requires "end-around carry"

Use cases:

• Not used in modern computers

Signed Magnitude

sign = 1
value = 000 101
→ 1000 0101

Problems:

• Two representations of zero: +0 = 0000 0000 –0 = 1000 0000
• Addition/subtraction is more complex in hardware

Use cases:

• Used today only in floating point formats (for the sign bit)