Carry-Lookahead Adder

The Carry-Lookahead Adder (CLA) 16-bits Adder is a type of digital circuit that improves upon the performance of a standard ripple-carry adder by reducing the propagation delay caused by carry bits.

Full Adder

A full adder is the building block of a CLA, which performs the addition of three bits: two significant bits and one carry-in bit (Cin). It produces a sum bit and a carry-out bit (Cout), where:

• $\text{Sum} = A \oplus B \oplus C_{in}$
• $C_{out} = (A \land B) \lor (B \land C_{in}) \lor (A \land C_{in})$

CLA4

A 4-bit CLA uses full adders by generating and propagating carry bits without waiting for carry-out from the previous stage. This is achieved by introducing two signals for each bit position:

• $G$ (Generate): Indicates if a carry bit will be generated.
• $P$ (Propagate): Indicates if a carry bit will be propagated.

The carry bits are calculated using these signals, which allows the CLA to determine carry bits in parallel.

CLA16

For the 16-bit CLA, four 4-bit CLA blocks are interconnected, each block responsible for a group of 4 bits. The CLA16 extends the concept of carry generation and propagation across 16 bits, making it suitable for larger binary numbers.

Signals for 16-bit CLA

The key signals $G_i$ and $P_i$ are used for the ith group of bits, where:

• $G_i$: True if the ith group generates a carry.
• $P_i$: True if the ith group can propagate a carry.

These signals allow the calculation of the carry bits ($C_{i+1}$) for each group using logical equations.

Advantages of CLA

• Quick Carry Calculation: Carry bits are determined without sequential dependency.
• Latency Reduction: Parallel calculation of carry bits reduces overall latency.
• Scalability: CLA scales efficiently for larger binary numbers.

Testing and Validation

The CLA circuit is tested using various input cases to ensure its correct operation under different conditions such as random values, boundary conditions, and specific binary patterns.

Implementation Details:

• Product Family: Target FPGA device family, e.g., "artix7".
• Target Device: Specific FPGA model used for synthesis.
• Timing: Design constraints for clock frequency and propagation delay.

Ports and Interface:

• a and b: Operand inputs for the addition operation.
• cin: Input carry bit (carry-in).
• sum: Output port for the result of addition.
• cout: Output carry bit (carry-out).