To understand the functioning of a 3-to-8 line decoder:

• (A) Enable input is set to 1.
• (C) Apply the 3-bit binary input.
• (D) Decoder converts the 3-bit input into 8 possible outputs.
• (B) Finally, one of the 8 output lines is activated based on the input code.

✅ Therefore, the correct sequence is: \[ (A), (C), (D), (B) \]

We know the relationship between minimum Hamming distance \(d_{\min}\) and error correction capability \(p\):

\[ d_{\min} \;\geq\; 2p + 1 \]

This ensures the code can correct up to \(p\) errors.

✅ Correct answer:

\[ \boxed{2p+1} \]

JK Flip-Flop Truth Table (Inputs → Next State)

• (A) 0 0 → (IV) No Change
• (B) 0 1 → (III) Reset
• (C) 1 0 → (II) Set
• (D) 1 1 → (I) Toggle

✅ Correct Answer: Option 2

To implement an \(n:1\) multiplexer using only \(2:1\) multiplexers, the minimum number required is:

\[ \text{Number of 2:1 MUX} = n - 1 \]

For \(n = 16\):

\[ 16 - 1 = 15 \]

✅ Therefore, the minimum number of \(2:1\) multiplexers required to design a \(16:1\) multiplexer is: \[ \boxed{15} \]

Solution

(A). ✅ Correct. Combinational logic circuits do not have memory. Sequential circuits include memory elements.

(B). ❌ Incorrect. Sequential circuits depend on both current and past inputs (via memory), while combinational circuits depend only on current inputs.

(C). ❌ Incorrect. Flip-flops and latches are examples of sequential circuits, not combinational circuits.

(D). ✅ Correct. Multiplexer (MUX) is a combinational logic circuit.

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Correct Statements: (A) and (D)

Answer: Option 1

A circuit that adds two 1-bit numbers and produces outputs for Sum and Carry but does not handle carry input is called a Half Adder.

A	B	Sum (A⊕B)	Carry (A·B)
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Boolean Expressions:

• Sum = \( A \oplus B \)
• Carry = \( A \cdot B \)

Final Answer: The circuit is a Half Adder.