Question

The gates required to build a full adder are :

• A. 2 Ex-OR gate, 2 AND gate and 1 NOT gate
• B. 2 Ex-OR gate, and 2 AND gate
• C. 2 Ex-OR gate, 2 AND gate and OR gate
• D. 2 Ex-OR gate

Hint:

A full adder can also be constructed using:
• Two half adders
• One OR gate Remember: \[ \text{Full Adder} = 2\ \text{Half Adders} + 1\ \text{OR gate} \]

Answer 1

The Correct Option is C

Concept: A full adder is a combinational digital circuit used to perform addition of three binary bits: \[ A,\ B,\ \text{and}\ C_{in} \] The outputs of a full adder are:
• Sum output \((S)\)
• Carry output \((C_{out})\) The Boolean expressions of a full adder are: :contentReference[oaicite:0]{index=0} and :contentReference[oaicite:1]{index=1} From these expressions, we can determine the number and type of gates required.

Step 1: Determine gates required for SUM output. The SUM expression is: \[ S=A\oplus B\oplus C_{in} \] To implement this:
• First XOR gate computes: \[ A\oplus B \]
• Second XOR gate computes: \[ (A\oplus B)\oplus C_{in} \] Therefore: \[ \text{Number of XOR gates required} = 2 \]

Step 2: Determine gates required for carry output. Carry expression: \[ C_{out}=AB+C_{in}(A\oplus B) \] This expression contains:
• One AND gate for: \[ AB \]
• One AND gate for: \[ C_{in}(A\oplus B) \] Thus: \[ \text{Number of AND gates required} = 2 \]

Step 3: Determine final combining gate. The two AND outputs must be added logically. That requires: \[ AB + C_{in}(A\oplus B) \] The logical addition operation is performed using: \[ \text{OR gate} \] Hence: \[ \text{One OR gate is required} \]

Step 4: Count total gates. Total gates required:
• 2 XOR gates
• 2 AND gates
• 1 OR gate Thus the correct option is: \[ \boxed{\text{2 Ex-OR gate, 2 AND gate and OR gate}} \]

Step 5: Write final answer. Hence the correct answer is: \[ \boxed{(C)} \]