Question 10.29: Describe in details ‘look-ahead carry’....
Describe in details ‘look-ahead carry’.
One method of speeding up the addition process, by eliminating this ripple carry delay, is called look-aheadcarry addition. This method is based on two functions of the full-adder, called the carry generate (CG) and carry propagate (\mathrm{CP}) functions.
The CG function indicates when an output carry is generated by the full-adder. A carry is generated only when both inputs bits are 1 s. This condition is expressed as the AND function of the two inputs bits P and Q :
C G=P Q 10.5
A carry input may be propagated by the full-adder when either or both of the input bits are 1 s. This condition is expressed as the OR function of the input bits P and Q :
C P=P+Q 10.6
The carry generate and carry propagate conditions are illustrated in Fig. 10.22.
How can the carry output of a full-adder be expressed in terms of the carry generate (\mathrm{CG}) and the carry propagate (\mathrm{CP}) ? The output carry (\mathrm{CO}) is a 1 if the carry generate is a 1 OR if the carry propagate is a 1 AND the input carry (\mathrm{CI}) is a 1 . In other words, we get an output carry of 1 if it is generated by the full-adder (P=1 AND Q=1) or if the adder can propagate the input carry (P=1 OR Q=1) and C_{\text {in }}=1. This relationship is expressed as
C O=C G+C P \cdot C I 10.7
