# CSCI 255, ENGR 274, ECE 212 -- 12 October, 2000

## Announcements

• generate, if both bits are 1
• gi = xi yi
• propagate, if one bit is 1
• pi = xi XOR yi
• pi = xi + yi
• carry out, if generating or propagating a carry in
• ci+1 = gi + pi ci
• doing the math
• ci+1 = gi + pi ci
• ci+2 = gi+1 + pi+1 gi + pi+1 pi ci
• ci+3 = gi+2 + pi+2 gi+1 + pi+2 pi+1 gi + pi+2 pi+1 pi ci
• ci+4 = gi+3 + pi+3 gi+2 + pi+3 pi+2 gi+1 + pi+3 pi+2 pi+1 gi + pi+3 pi+2 pi+1 pi ci
• grouping some results
• gi,i+3 = gi+3 + pi+3 gi+2 + pi+3 pi+2 gi+1 + pi+3 pi+2 pi+1 gi
• pi,i+3 = pi+3 pi+2 pi+1 pi ci
• ci+4 = gi,i+3 + pi,i+3 ci
• wire it together in Figure 5.14

## The ALU

• Arithmetic-Logic Unit
• Typical pins
• Two n-bit input words
• One carry-in input
• One n-bit output word
• One carry-out output
• Control inputs
• 4 bit TTL ALU

## Combinational multipliers

• The Full Multi
• Partial products
• A15..0 = A15..8 A7..0
• B15..0 = B15..8 B7..0
• A15..0 × B15..0 = (A15..8 × B15..8) << 16 + (A15..8 × B7..0 + A7..0 × B15..8) << 8 + (A7..0 × B7..0)