CUET PG 2021 — Computer PYQ
CUET PG | Computer | 2021How many full adder and half adder are required to add 16- bit numbers?
Choose the correct answer:
- A. 8 half adders, 8 full adders
- B. 1 half adder, 15 full adders(Correct Answer)
- C. 16 half adders, no full adder
- D. 4 half adders, 12 full adders
1 half adder, 15 full adders
Explanation
1. The Standard Efficient Configuration
To add the first (LSB) bits, no carry-in is required from a previous stage, so a Half Adder is sufficient. For the remaining bits, Full Adders are required to process the carry.
The Logic Equation:
Total Bits (n)=16
Half Adders (HA)=1
Full Adders (FA)=n−1
Substituting the value:
Full Adders (FA)=16−1=15
2. The Universal Configuration
In some designs (especially modular ones), every stage is a Full Adder, and the carry-in (Cin) of the first stage is simply connected to ground (logic 0).
The Equation:
Full Adders (FA)=n=16
Half Adders (HA)=0
Summary Table (Standard 16-bit Ripple Carry Adder)
| Component | Quantity Required | Purpose |
| Half Adder (HA) | 1 | Adds the Least Significant Bit (LSB) |
| Full Adder (FA) | 15 | Adds the remaining 15 bits with carry-in |
| Total Outputs | 16 Sum bits+1 Carry bit | The result of the addition |
Final Answer:
For a 16-bit adder, the most common answer is:
15 Full Adders+1 Half Adder