Question

Given below are two statements :
one is labelled as
Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) :
In a ripple carry adder, carry propagation delay increases linearly with the number of bits.
Reason (R) :
Each bit addition must wait for the carry output from the previous stage.
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

To fix this "linear" bottleneck, modern CPUs use Carry Look-ahead Adders (CLA), which calculate carries in parallel using logic, making the delay logarithmic instead of linear.

Answer 1

The Correct Option is A

Concept:
• A Ripple Carry Adder (RCA) is a digital circuit that produces the arithmetic sum of two binary numbers.
• It is constructed by cascading several full adders in series.

Step 1: Analyze the structure of an RCA
In an \(n\)-bit RCA, the first full adder computes the sum of the LSBs.
The carry generated by the \(i^{th}\) bit addition is fed as the input carry (\(C_{in}\)) to the \((i+1)^{th}\) bit addition.
This creates a chain where each stage depends on the completion of the previous one.

Step 2: Calculate the propagation delay
If \(\Delta t\) is the delay of a single full adder stage to produce a carry:
Total delay \(T \approx n \times \Delta t\).
Since \(T\) is directly proportional to \(n\), the delay increases linearly.
Assertion (A) is correct.

Step 3: Verify the causal link
The reason the delay is linear is exactly because of the serial dependency described in Step 1.
Reason (R) correctly describes this "wait" condition.
Thus, (R) is the correct explanation for (A).