177k views
1 vote
The circuit below is a carry-lookahead 2- bit adder Compare the cost and propagation delay of this circuit to that of a ripple-carry 2-bit adder. -In this scenario, cost is defined as the total number of gates, plus the total number of gate inputs. -The propagation delay is the number of gates along the critical path. How would propagation delay change in each implementation if we were adding more than 2 bits?

1 Answer

5 votes

Final answer:

A ripple-carry 2-bit adder usually has a lower cost due to simpler design, but a carry-lookahead adder provides a significantly shorter propagation delay. When adding more bits, the ripple-carry adder's delay increases linearly, whereas the carry-lookahead adder's delay increases less significantly.

Step-by-step explanation:

Comparing the cost and propagation delay of a carry-lookahead 2-bit adder versus a ripple-carry 2-bit adder involves different aspects of circuit design. In terms of cost, defined as the total number of gates plus the total number of gate inputs, a ripple-carry adder tends to have a lower cost because it uses a simpler, linear chain of full adders. However, the carry-lookahead adder, despite potentially higher initial cost, significantly reduces propagation delay, as it computes the carry signals in advance using more complex logic. The critical path for a carry-lookahead adder is shorter because it does not wait for the carry to propagate through each bit of the adder as in the ripple-carry design.

As the number of bits increases, the propagation delay in a carry-lookahead adder increases less significantly compared to a ripple-carry adder. This is because a ripple-carry adder's delay increases linearly with each additional bit due to the need to wait for the carry to progress through the entire width of the adder, while a carry-lookahead adder is designed to mitigate this effect with more sophisticated carry computation logic.

User Jeremy Conley
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.