Final answer:
A 4-bit carry-lookahead adder has a significantly lower propagation delay than a 4-bit ripple-carry adder due to advanced carry computation.
The difference in propagation delay between a 16-bit carry-lookahead adder and a 16-bit ripple-carry adder is even more substantial, as the carry-lookahead adder is designed to optimize speed for larger bit-widths.
Step-by-step explanation:
The propagation delay of a 4-bit carry-lookahead adder (CLA) is significantly less than that of a 4-bit ripple-carry adder (RCA) due to the CLA's ability to calculate carry bits in advance, thereby reducing the overall delay in summing multiple bits. For a ripple-carry adder, the carry output from each bit addition must propagate through to the next, causing a delay that increases linearly with the number of bits.
However, the carry-lookahead logic generates carry values more quickly by using combinational logic, thus resulting in a faster addition operation.
When comparing a 16-bit carry-lookahead adder to a 16-bit ripple-carry adder, the difference in propagation delay is even more pronounced. The ripple-carry adder's delay grows linearly with the number of bits, while the carry-lookahead adder leverages a more sophisticated circuit design to process carries and can be constructed in multiple levels to optimize speed. This multi-level approach further increases its speed advantage over the basic ripple-carry adder for larger bit-widths.