Digital Design

Que 6: What is the range of n bit 2’s complement and 1’s complement representation?

Ans  6: 2’s complement represents an integer in the range [−2n−1, 2n−1 − 1].
        1’s complement represents an integer in the range [−2n−1 + 1, 2n−1 − 1].

Que 7: In which two input gate, If we toggle any one of the inputs toggles the output?

Ans  7: In gray code, only one bit toggles in the next number, for every next number output should toggle, there could be two possibilities.
Refer to Table 1 for Possible solutions at Outputs 1 and 2.
This can be concluded that Output 1 is XOR and Output 2 is XNOR.

Que 8: In 7 input XOR gate, If 4 inputs are 1 and 3 inputs are 0, what will be the output?

Ans  8: In the XOR gate, When Input has even number of 1’s gives output 0 and if Odd number of inputs are 1 then output is 1.
If 4 inputs are 1 and 3 inputs are 0, then output will be 0.

Que 9: Which gates are universal gates? Design XOR gates using NAND gate.

Ans  9: A universal gate is a gate that can implement any Boolean function without the need to use any other gate type. The NAND and NOR gates are universal gates.
Refer to the Figure, for XOR gate implementation from the NAND gate.

Que 10: Implement OR gate using NAND gate.

Ans  10: OR gate can be converted to NAND gate using De Morgan’s theorem.
                A + B  = ((A + B )’)’
                = (A’ . B’)’
                Refer to the Figure, For OR gate using NAND gate implementation.

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