- Look Ahead Carry Adder Definition: A look ahead carry adder is a type of adder circuit that minimizes delay by anticipating carry bits in advance.
- Working Principle: It determines carry bits by analyzing the input bits, reducing the delay found in traditional adders.
- Carry Propagation and Generation: Carry propagation (Pi) shows if a carry will move to the next bit, and carry generation (Gi) shows if a carry is created at the current bit.
- Equations for Carry and Sum: Specific equations based on Pi and Gi that depend only on the initial carry input (c0), not on previous carry stages.
- Comparison with Ripple Carry Adder: Look ahead carry adders are faster because they don’t rely on the previous stage’s carry term, unlike ripple carry adders.
We have seen that the parallel adder circuit built using a cascaded arrangement of full adders is highly affected by the delay associated with the propagation of carry bits (more on this in the article “Parallel Adder”). Greater the number of bits needed to be added, greater is the delay associated. If we need to get rid of this ‘delay’ problem, then we need to go for the design of Look Ahead Carry Adder circuit.
Working Principle of Look Ahead Carry Adder
To overcome ripple carry delay, we can anticipate carry bit generation in advance. By analyzing input bits early, we can determine if a carry will occur, reducing delay.
If the input bits are 0 and 0, 1 and 0, or 0 and 1, the sum is 0 or 1 with no carry. If both input bits are 1, the sum is 1 and a carry is generated. These cases assume the carry-in (ci) bit is 0. If ci is 1, a carry is generated for all input combinations except when both bits are 0.
Combining these two factors, it can be concluded that we would get our carry term 
under two situations: (i) when both of the input bits (ai, bi) are 1 or (ii) when any one of the input bits (ai, bi) is 1 and the carry obtained by adding the previous input bits (ci) is 1.
These statements can be equivalently represented in terms of logical expressions as
Collectively, the expression for the carry bit can be written as
However we have our logical expression for the sum kept as such i.e.
Next, let us denote 
by the term Pi called carry-propagation and 
by the term Gi called carry-generation. Thus the equations (i) and (ii) can be rewritten as
Specifically,
For i = 0, we have,
For i = 1, we have,
For i = 2, we have,
Generalizing, for i = n, we have,
The important factor to be noticed in all of the above expressions is the fact that the carry term of any particular stage depends only on the carry-input (c0) term apart from carry-generation and carry-propagation terms. Yes, only on c0 (a user provided input bit) and not the carry terms generated by its preceding stages. This is true irrespective of the stage to which they belong.
Unlike ripple carry adders, where the current stage’s carry depends on the previous stage’s carry, look ahead carry adders do not. This helps them overcome the delay seen in ripple carry adders.
The same reason enables look ahead adders to operate much faster in comparison to other kinds. However the price paid for it is the complexity involved in its hardware.
