Final answer:
The delay of a 4-bit ripple carry adder is calculated by summing the carry propagation delay through the full adders and the final sum delay. For each stage, the carry delay is 4δ and the sum delay in the last bit is 3δ, resulting in a total delay of 15δ.
Step-by-step explanation:
To calculate the delay of a 4-bit ripple carry adder, we need to analyze the path that the carry signal takes to propagate through the adder, as this usually dictates the overall delay. In a ripple carry adder, each bit addition relies on the carry from the previous bit. With an EX-OR gate delay of 3δ for each full adder, and other gates (including the carry-out which involves AND and OR gates) having a delay of 2δ, we calculate the delay as follows:
The carry-out of each bit has the longest delay path, which includes an AND gate and an OR gate (both with a 2δ delay). Thus, each carry generates a total delay of 4δ. However, since we have a ripple effect, the carries need to propagate through each of the previous stages. In a 4-bit adder, the fourth bit's carry would take a cumulative delay of 4δ * 3 (as the first bit does not need to wait for any previous carry), which equates to 12δ. Finally, adding the EX-OR delay for the sum in the fourth bit, which is 3δ, gives us the overall delay, totaling 15δ.