- 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.
The parallel adder circuit built by cascading full adders is limited by the delay associated with carrying propagation (more on this in the article “Parallel Adder”). The more bits to be added, the longer this delay becomes. The design of a Look Ahead Carry Adder circuit removes this delay problem.
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 bit is 0 or 1 with no carry. If both input bits are 1, the adder produces an output bit of 0 together with a generated carry. 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
The logical expression for the sum stays as it is, namely
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. It depends only on c0 (a user provided input bit) and on none of the carry terms generated by its preceding stages. This is true irrespective of the stage to which they belong.
A ripple carry adder waits on each previous stage’s carry before the next stage can settle; a look ahead carry adder computes every stage’s carry expression up front from the user-supplied input and the P/G terms instead. 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.
