Question

Implement switching function F (A, B, C) = ABC + BC + AB with a 4-to-1 multiplexer: show your assignment A, B, C. to data inputs (D3, D2, D1, D0) and select inputs (S1, S0) of the 4-to-1 multiplexer. A single inverter is available if needed. Obtain the circuit schematic using the 4-to-1 mux and inverter as building blocks.

Answer 1

Step-by-step explanation:

`\mathbf{F(A, B, C) = \bar A \bar B C + B \bar C + AB}`

`\mathbf{F(A, B, C) = \bar A \bar B C + AB \bar C + \bar A B \bar C + ABC + AB \bar C}`

`\mathbf{F(A, B, C) = 001,110,010,111,110}`

Hence;

`\mathbf{F(A, B, C) = \sum m (1,2,6.7)}`

`\mathbf{ A \ \ \ B \ \ \ C \ \ \ \ \ \ \ F } \\ \\ \mathbf{ 0 \ \ \ \ 0 \ \ \ \ 0 \ \ \ \ \ \ \ 0 } \\ \\ \mathbf{ 0 \ \ \ \ 0 \ \ \ \ 1 \ \ \ \ \ \ \ 1 }\to \ \ D_0 = C \\ \\ \mathbf{ 0 \ \ \ \ 1 \ \ \ \ 0 \ \ \ \ \ \ \ 1 } \to \ \ D_1 = \bar C \\ \\ \mathbf{ 0 \ \ \ \ 1 \ \ \ \ 1 \ \ \ \ \ \ \ 0 } \\ \\ \mathbf{ 1 \ \ \ \ 0 \ \ \ \ 0 \ \ \ \ \ \ \ 0 } \\ \\ \mathbf{ 1 \ \ \ \ 0 \ \ \ \ 1 \ \ \ \ \ \ \ 0 }`

`\\ \\ \mathbf{ 1 \ \ \ \ 1 \ \ \ \ 0 \ \ \ \ \ \ \ 0 } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to D_3 = 1 \ \ ; D_2 = 0 \\ \\ \mathbf{ 1 \ \ \ \ 1 \ \ \ \ 1 \ \ \ \ \ \ \ 1 }`

The 4-to-1 MUX and inverter is shown in the attached file below.