Question

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?

Answer 1

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.