negative numbers _ sign-magnitude + twos-complement + sign extension & truncation

sign-magnitude representation

• consists of 2 parts: sign and magnitude
• decimal example: $+123_{10}$ and $-123_{10}$
• binary example: $01100_2=+12_{10},11100_2=-12_{10}$
  • sign represented by MSB (most significant bit = leftmost digit): 1 = negative, 0 = positive

two’s complement representation

• positive numbers represented as usual
• leading 1’s for negative numbers
• to negate any number
  • flip all the bits
  • add 1 to the least significant bit (LSB = rightmost digit)