Computer Science – 3.2 Logic Gates and Logic Circuits | e-Consult
3.2 Logic Gates and Logic Circuits (1 questions)
a) Boolean Expression using only NAND gates:
We need to convert the given expression to use only NAND gates. Recall that:
- NAND(X) = NOT(X AND NOT(X))
- NOT(X) = NAND(X, X)
- NOR(X, Y) = NAND(NAND(X, Y), NAND(X, Y))
Y = (A AND B) NOR C
Y = NAND(NAND(A, B), NAND(A, B)) NAND C
b) Logic Circuit Diagram:
The circuit diagram should consist of:
- Two NAND gates with inputs A and B.
- A NAND gate with inputs the outputs of the two NAND gates.
- A NAND gate with inputs the output of the previous NAND gate and C.
Diagram (cannot be directly rendered in HTML, but would be a visual representation of the described gates connected as described).
c) Convenience of using NAND gates:
Using NAND gates is a convenient way to construct digital circuits because NAND gates are considered universal gates. This means that any Boolean function can be implemented using only NAND gates. This simplifies circuit design and manufacturing, as only one type of gate is required. It also reduces the number of different components that need to be stocked and handled.