Two's Complement

Description:

• Representing signed integers (both positive and negative numbers) in binary form, where the most significant bit (MSB) signifies the sign as well as the supposed value but negative
  • ex: $1011_2=-8+2+1=-5$

Signed extension & truncation:

• Given MSB is 1, more $1$s added in the most left doesnt change its value.
  • Same as $0$
  • ex: $1011_2=111011_2=-32+16+8+2+1=5$
• But truncation will not change value if the MSB is not 1

Calculation:

• Much simplier than Signed integer
• Given B1+B2
• Addition:
  1. Convert negative numbers to their two’s complement form.
  2. Perform regular binary addition.
  3. If there’s an overflow (carry-out from the MSB), the result overflows and might need correction depending on the specific application.
• Subtraction:
  1. Negate the subtrahend (the number being subtracted) by taking its two’s complement.
  2. Perform addition as described above.