Carry Look Ahead Adder

Ripple Carry Adder

Ripple carry adders add the two bits instantly, but each adder block has to wait for the carry bit that arrives from the previous block. So, in case of ripple carry adders it is not possible to find the sum for any block until the input carry is known. Hence, there happen to be a time delay, i.e., carry propagation delay.

In such a case, when the number of adder blocks are increased, the delay increases and situation gets worse.

    

Carry look-ahead adder(CLA)

The carry look-ahead adder solves the carry delay problem that occurs in ripple carry adder. Carry look-ahead adder calculates the carry signal in advance, based on the input signals. Carry look ahead adders provide a faster way to add two binary numbers and reduce the computation time. They create two signals Carry Propagator and Carry Generator. The Carry Propagator is propagated to the next level where as the carry generator generates output carry, regardless of the input carry.  

Design of CLA

The boolean expressions used to construct a carry look-ahead adder are given below. First we need to generate the two signal Carry Propagator (P) and Carry Generator (G),

Pᵢ = aᵢ ⊕ bᵢ

Gᵢ =  aᵢ.bᵢ

The output sum and carry can be expressed as:

Sum = Pᵢ ⊕ cᵢ

cᵢ₊₁ = Gᵢ + (P - cᵢ)

 

We can now easily design the circuit, and write the Boolean function for the carry output of each stage.

C₁ = G₀ + P₀.c₀

C₂ = G₁ + P₁.c₁ = G₁ + P₁G₀ + P₁P₀c₀

C₃ = G₂ + P₂.c₂ = G₂ + P₂G₁ + P₂P₁G₀ + P₂P₁P₀c₀

C₄ = G₃ + P₃.c₃ = G₃ + P₃G₂ + P₃P₂G₁ + P₃P₂P₁G₀ + P₃P₂P₁P₀c₀

Advantages of CLA

1. Reduction of propagation delay. 
2. Provision of fastest addition logic function.

Disadvantages of CLA

1. As number of variables get increasing, the CLA gets more and more complicated.
2. More costlier as number of hardware used increases.