Group generate and propagate

source this playlist on arithmetic circuits.

Introduction

• Examining the expressions for carry outs at different bit positions we see patterns
• last term contains carry in and only propagates, all the terms before it contains generate bits and propagate bits not carry in

Group propagate

• means that the range of the bit positions you are describing is all propagating
• the product of all the propagates in the range

Group generate

• means within the range of bits
• some bit position one or more is generating a carry out
• and this carry out has enough propagates active so that it can show at the output

Carry at any position

• CarryX = Group0:X + P0:X Cin
• Carry3:5 = Group 3:5 + P3:5 C2
  • this means either carry 2 is propagating to carry 5 or there is a generated carry in range 3 : 5 which manages to propagate to C5

Dot operator

• acts on ranges of group generate and propagate to combine them
• doesn’t work on ranges that have gaps
• the order of operands is important
• Implemented using
  • two cmos gates the produce the resultant group propagate (AND gate)
  • sum of product that gives you the group generate