Let F(x2; x1; x0) be a boolean function with the following specication: - F(x2;

Question

Let F(x2; x1; x0) be a boolean function with the following specication:

- F(x2; x1; x0) = 1, if the decimal value of the binary number (x2x1x0)2 is a multiple of 5;

- F(x2; x1; x0) = 0, otherwise.

Perform the following operations:

(a) Fill in the truth table for F(x2; x1; x0):

(b) Based on the truth table above, generate the corresponding boolean expression for F(x2; x1; x0) andsimplify it as much as possible using Boolean algebra laws;

(c) Using ONLY 2-input AND and OR gates and inverters (i.e. NOT gates), build the digital circuitimplementing F(x2; x1; x0) (you may use the simplied form derived in (b));

(d) Show how to implement F(x2; x1; x0) using ONLY the 8-to-1 multiplexer below:

Let F(x2; x1; x0) be a boolean function with the following specication: - F(x2; x1; x0) = 1, if the decimal value of the binary number (x2x1x0)2 is a multiple of 5; - F(x2; x1; x0) = 0, otherwise. Perform the following operations: (a) Fill in the truth table for F(x2; x1; x0): (b) Based on the truth table above, generate the corresponding boolean expression for F(x2; x1; x0) andsimplify it as much as possible using Boolean algebra laws; (c) Using ONLY 2-input AND and OR gates and inverters (i.e. NOT gates), build the digital circuitimplementing F(x2; x1; x0) (you may use the simplied form derived in (b)); (d) Show how to implement F(x2; x1; x0) using ONLY the 8-to-1 multiplexer below:

Explanation / Answer

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F = (x2' x1' x0' ) + ( x2 x1' x0)

F = x1' (x2' x0' + x2 x0 )

Here is the circuit

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