Number Representation

How do we represent signed (positive & negative) numbers?

Option 3: Two's Complement ☜ ✓ ★ ☺

• Flip every bit to represent the number's negative value, then add one
  (Note: surprisingly, this also works both ways!)
• Left-most bit still represents the sign
• Examples:

          00000001  = +1
          11111111  = -1   (two's complement)
  
          00000101  = +5
          11111011  = -5   (two's complement)
  
          01111111  = +127
          10000001  = -127   (two's complement)

• Problem 1 Solved!

          00000000  = +0
          00000000  = -0   (two's complement)

• Problem 2 Solved!

           00000101     5
           11111111  + -1
           --------  -----
          100000100     4  (ignore overflow)