Consider the following.

f(a, b, c, d, e) =

m(2, 3, 6, 12, 13, 16, 17, 18, 19, 22, 24, 25, 27, 28, 29, 31)

(a)

Find a minimum two-level NOR-gate circuit to realize f. (Enter the corresponding logical expression. Use the following as necessary: a, b, c, d, e.)

f(a, b, c, d, e) =

For the diagram, submit a drawing

(b)

Find a minimum three-level NOR-gate circuit to realize f. (Draw the circuit diagram and then enter the corresponding logical expression. Use the following as necessary: a, b, c, d, e.)

Correct Answer For B-

A logic circuit has 6 gates and 16 inputs. The circuit will be read from the final output to the inputs.

1. The final nor gate has output f and three inputs.
   1. The first input to the final nor gate is the output from a nor gate.
      1. The nor gate has three inputs.
         1. The first input to the nor gate is the output from a nor gate.
            1. The nor gate has two inputs.
               1. The first input to the nor gate is a'.
               2. The second input to the nor gate is e'.
         2. The second input to the nor gate is b'.
         3. The third input to the nor gate is d'.
   2. The second input to the final nor gate is the output from a nor gate.
      1. The nor gate has three inputs.
         1. The first input to the nor gate is a.
         2. The second input to the nor gate is c.
         3. The third input to the nor gate is d.
   3. The third input to the final nor gate is the output from a nor gate.
      1. The nor gate has three inputs.
         1. The first input to the nor gate is b.
         2. The second input to the nor gate is c'.
         3. The third input to the nor gate is the output from a nor gate.
            1. The nor gate has two inputs.
               1. The first input to the nor gate is e.
               2. The second input to the nor gate is d'.

(C) f(a, b, c, d, e) =

a c d d