4-Bit Carry-Select Adder
High-performance arithmetic units must minimize the critical path delay caused by carry propagation. By precomputing multiple possible sums in parallel and selecting the correct one once the true carry-in arrives, the critical path is reduced to a single multiplexer delay.
The circuit takes two 4-bit inputs A and B, and a 1-bit carry-in Cin. It produces a 4-bit sum S and a 1-bit carry-out Cout. The calculation S = A + B + Cin must be performed using a carry-select architecture. Two separate 4-bit adders must evaluate the sum simultaneously: one assuming a carry-in of 0, and the other assuming a carry-in of 1.
Key behavioral cases:
| Cin | A (decimal) | B (decimal) | Cout | S (decimal) | |-------|---------------|---------------|--------|---------------| | 0 | 5 | 5 | 0 | 10 | | 1 | 15 | 0 | 1 | 0 | | 0 | 10 | 10 | 1 | 4 | | 1 | 15 | 15 | 1 | 15 |
Constraints
- Use exactly two complete 4-bit adders computing in parallel.
- Hardwire the carry-in of the first 4-bit adder to 0.
- Hardwire the carry-in of the second 4-bit adder to 1.
- Use multiplexers to select the final
SandCoutbased on the actualCin. - Combinational logic only.
Topics
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