carry look ahead adder vs ripple carry

Question

$Exclusive-OR$ gate has a propagation delay of $10$ ns and that the $AND$ or $OR$ gates have a propagation delay of $5$ ns.What is the total propagation delay time in the four-bit adder.Assume $FAN-IN =2$

$1)$ ripple adder

$2)$ carry look ahead adder

Comments

Kindly mention the FAN IN of the logical gates to be used.

Answer 1

1. Ripple carry adder
Tcarry= 4*(5+5)=40
Tsum=(4-1)*(5+5)+2*10=50
Total propagation delay=40+50=90 ns

Carry look ahead adder

TSUM = Pi+Ci

.              = Exor+ and+or+exor gate  time

.              = 10+5+5+10=30 ns

 

Comments

@iarnav getting same 80 for rca

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I think 3*20 + 20 =  80 for RCA

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This definitely seems incorrect.

If in the worst case we consider non-parallel execution of adders in ripple-ahead, even then it will require 4*20ns=80ns.

Whereas in parallel execution, it will be 50ns.

$c_{3}$  will reach last adder after 40ns and by that time we would have already done half of the sum in that last adder, so additional 10ns. Therefore 50ns.

In case of look-ahead generator we need 3 level and-or gate logic because of 2 fan-in.

Therefore, total 10+5+5+5+10 = 35ns.