Question

1) Implement the function F(A,B,C)=A+B′C (Show all solution details, Label your components, inputs, and outputs and their connections):

a. Using a single Decoder of minimum size + a single Gate of minimum number of inputs. [4 marks]
b. Using a single 4-to-16 Decoder + a single Gate of minimum number of inputs. [2 marks]
c. Using a single MUX with minimum size and nothing else (no gates at all). [4 marks]
d. Using a single 16-to-1 MUX and nothing else (no gates at all).

Answer 1

To implement the function F(A,B,C)=A+B′C using different components, follow the given steps.

Step-by-step explanation:

a. To implement the function F(A,B,C)=A+B′C using a single Decoder of minimum size and a single Gate of minimum number of inputs, follow these steps:

1. Label the inputs as A, B, and C.
2. Connect input C directly to the Gate.
3. Connect input A to the Decoder.
4. Connect the output of the Decoder to the Gate.
5. Connect input B to the Gate via an inverter.

b. To implement the function using a single 4-to-16 Decoder and a single Gate of minimum number of inputs, follow the same steps as in part a, but connect input B directly to the Decoder instead of using an inverter.

c. To implement the function using a single MUX with minimum size, connect input A directly to the select input of the MUX, input B to one of the data inputs, and the negation of input C to the other data input.

d. To implement the function using a single 16-to-1 MUX, connect inputs A and B to the select inputs of the MUX, and connect input C to one of the data inputs. Connect the remaining 15 data inputs to 0 units.