determine the values of gi, pi, and ci for each of the casesbelow, assuming each value is represented using 4 bits: i. 4 +4

ii. 8 - 2

iii. (-3) - (-7)

iv. 9 + 10

v. -8 + 7

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Multi-level CLA ■ Solution: do two levels of carry lookahead First level generates Result (using carry lookahead to generate the internal carries) and propagate and generate signals for a group of 4 bits (Pi and Gi) 3/16/2015 Second level generates carry outs for each group based on carry in and Pi and Gi from previous group C16 X3 Y3 7 = 0111 -3=1101 Block 3 C12 S3 CLA example ▪ 7+ (-3) go=1.1=1 g₁=1.0=0 9₂=1-1=1 93 0.1 0 X2 Y2 C8 Block 2 P2|G2| 22|G₂||$2 X1 Y1 Block 1 Carry lookahead logic CES 273 Lecture 10 Po=1+1=1 P₁ = 1+0=1 P₂ = 1 + 1 = 1 0+1=1 P3 = C₁ = go + Poin = 1+1.0=1+0=1 C₂=9₁ +P₁C₁ = 0+1.1 = 0+1=1 C₂ = 9₂ + P₂C₂=1+1-1=1+1=1 C4 = 93 + P3C3 = 0+1 -1 = 0+1=1 XO YO CA Block 0 CO SO 17 CLA example ■ Given the following operations: 7+(-3) 3-4 ▪ Assuming each number uses 4 bits, calculate g, and p, for each bit C₁+1 (carry out) for each bit 3/16/2015 CLA example 3-4 CES 273 Lecture 10 3= 0011 4 0100... but we're subtracting! ■ b input = ~(4) = -(0100) = 1011, carry in = 1 1.1=1 go g₁ = 1.1=1 g₂=0.0=0 93=0.1=0 Po = 1+1=1 P₁ = 1+1=1 P₂ = 0+0=0 P3 = 0+1=1 C₁ = go + PoCin= 1+1-1=1+1=1 C₂ = 9₁ + P₁C₁ = 1+1-1=1+1=1 C₂ = 9₂ + P₂C₂ = 0+0.1=0+0=0 C4 93 + P3C3 = 0+1.0 = 0+0=0 18 Multi-level CLA ■ Solution: do two levels of carry lookahead First level generates Result (using carry lookahead to generate the internal carries) and propagate and generate signals for a group of 4 bits (Pi and Gi) 3/16/2015 Second level generates carry outs for each group based on carry in and Pi and Gi from previous group C16 X3 Y3 7 = 0111 -3=1101 Block 3 C12 S3 CLA example ▪ 7+ (-3) go=1.1=1 g₁=1.0=0 9₂=1-1=1 93 0.1 0 X2 Y2 C8 Block 2 P2|G2| 22|G₂||$2 X1 Y1 Block 1 Carry lookahead logic CES 273 Lecture 10 Po=1+1=1 P₁ = 1+0=1 P₂ = 1 + 1 = 1 0+1=1 P3 = C₁ = go + Poin = 1+1.0=1+0=1 C₂=9₁ +P₁C₁ = 0+1.1 = 0+1=1 C₂ = 9₂ + P₂C₂=1+1-1=1+1=1 C4 = 93 + P3C3 = 0+1 -1 = 0+1=1 XO YO CA Block 0 CO SO 17 CLA example ■ Given the following operations: 7+(-3) 3-4 ▪ Assuming each number uses 4 bits, calculate g, and p, for each bit C₁+1 (carry out) for each bit 3/16/2015 CLA example 3-4 CES 273 Lecture 10 3= 0011 4 0100... but we're subtracting! ■ b input = ~(4) = -(0100) = 1011, carry in = 1 1.1=1 go g₁ = 1.1=1 g₂=0.0=0 93=0.1=0 Po = 1+1=1 P₁ = 1+1=1 P₂ = 0+0=0 P3 = 0+1=1 C₁ = go + PoCin= 1+1-1=1+1=1 C₂ = 9₁ + P₁C₁ = 1+1-1=1+1=1 C₂ = 9₂ + P₂C₂ = 0+0.1=0+0=0 C4 93 + P3C3 = 0+1.0 = 0+0=0 18