CSCI 255, ENGR 274, ECE 212 -- 10 October, 2000

Announcements

• Quiz 1 solution

Representation of negative numbers -- review?

• Does 0 == -0?
• Do even numbers end with 0's
• Are both n and -n represented?
• Are there special rules for adding positive and negative numbers?

Signed Magnitude

Ones Complement

Twos Complement

Conversion to n-bit twos complement

• Convert to a n-bit binary number -- Use leading zero's if nexcessary!
• If positive,
  • Do nothing more!
• If negative,
  1. Complement the number
  2. Add one
• How about a spreadsheet?

Binary addition

Implementation of ripple-carry adder/subtractor

• Half-adder
• Full adder
  • s_i = x_i y_i XOR c_i
  • c_i+1 = x_i y_i + c_i x_i + c_i y_i
• Adding and subtracting
• Detecting overflow
  • Overflow occurs when the last two carries differ
• Performance of the ripple-carry adder
  • Composed to full adders
  • Has significant propagation delay

carry-select adder

Just do the top half twice, and select the right result