Digital Quiz-2

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📘 Half Adder - Notes

🔹 Definition

A Half Adder is a basic combinational logic circuit that performs the addition of two binary digits. It has two inputs — A and B — and produces two outputs: Sum (S) and Carry (C).

🔹 Binary Addition Process

The rules for binary addition of single bits are:

\( 0 + 0 = 0 \) (Sum = 0, Carry = 0)
\( 0 + 1 = 1 \) (Sum = 1, Carry = 0)
\( 1 + 0 = 1 \) (Sum = 1, Carry = 0)
\( 1 + 1 = 10 \) (Sum = 0, Carry = 1)

🔹 Truth Table

A	B	Sum (S)	Carry (C)	Justification
0	0	0	0	0 + 0 = 0
0	1	1	0	0 + 1 = 1
1	0	1	0	1 + 0 = 1
1	1	0	1	1 + 1 = 10

🔹 Sum and Carry Expressions (SOP)

From the truth table:

Sum = 1 when (A=0, B=1) and (A=1, B=0):

\[ S = A'B + AB' \]

Carry = 1 only when (A=1, B=1):

\[ C = AB \]

Hence:

\( S = A \oplus B \)
\( C = A \cdot B \)

🔹 Half Adder Implementation Using XOR and AND

This is the basic and most common implementation using standard logic gates:

🔹 Half Adder Implementation Using NAND Gates Only

Using only NAND gates, we can derive the same logic:

🔹 Half Adder Implementation Using NOR Gates Only

Similarly, the Half Adder can be built using only NOR gates:

🧠 Multiple Choice Questions – Half Adder

Q1. What are the two outputs of a Half Adder?

Sum and Carry
Carry and Borrow
Sum and Difference
Only Sum

Q2. What is the symbolic Boolean expression for the Sum output of a Half Adder?

\( A \cdot B \)
\( A + B \)
\( AB' + A'B \)
\( A \oplus B \)

Q3. What is the Carry output when A = 1 and B = 1?

0
1
A
B

Q4. The Half Adder circuit cannot:

Add carry from previous stages
Add two bits
Produce a carry
Compute XOR

Q5. Which gate alone can be used to implement a Half Adder?

OR
XOR
AND
NAND

Q6. What is the Carry expression in SOP form?

\( A + B \)
\( A \cdot B \)
\( A'B + AB' \)
\( A \oplus B \)

Q7. If A = 0 and B = 1, what is the Sum output?

0
1
Undefined
Can't say

Q8. The gate used for generating the Carry output is:

OR
NOT
AND
XOR

Q9. Which combination correctly represents a Half Adder using basic gates?

XOR and AND
OR and AND
XOR and OR
NAND and NOR

Q10. What is the Sum output when both A and B are 1?

1
0
A
B