Question

Implement the following functions with two-level NAND gate circuits:

a. f(a, b, c, d) = a'b'c + a'bc + abc
b. f(a, b, c, d) = a'cd' + a'bd + abd + ab'cd
c. f(a, b, c, d) = ab'd' + ad + a'bd + d
d. f(w, x, y, z) = wx'y' + wy'z' + xy'

Answer 1

To implement the given functions with two-level NAND gate circuits, you can use De Morgan's theorem to convert the given expressions to NAND gates.

Step-by-step explanation:

To implement the given functions with two-level NAND gate circuits, we can use De Morgan's theorem to convert the given expressions to NAND gates. Here's how:

a. f(a, b, c, d) = a'b'c + a'bc + abc

1. Apply De Morgan's theorem to the first term: (a'b'c)' = (a + b + c)'
2. Apply De Morgan's theorem to the other terms: (a'bc)' = (a' + b' + c')
3. Use NAND gates to implement the new expressions obtained in steps 1 and 2
4. Combine the outputs of the NAND gates using another NAND gate to get the final output, f(a, b, c, d)

b. f(a, b, c, d) = a'cd' + a'bd + abd + ab'cd

1. Apply De Morgan's theorem to each term to get a new expression using NAND gates
2. Use NAND gates to implement the new expression

c. f(a, b, c, d) = ab'd' + ad + a'bd + d

1. Apply De Morgan's theorem to each term to get a new expression using NAND gates
2. Use NAND gates to implement the new expression

d. f(w, x, y, z) = wx'y' + wy'z' + xy'

1. Apply De Morgan's theorem to each term to get a new expression using NAND gates
2. Use NAND gates to implement the new expression