Question

(a) Implement the following function using only 2-to-1 MUXes:

R = ab′h′ + bch′ + eg′h + fgh.
(b) Repeat using only tri-state buffers.

Answer 1

(a)
`\( R = ab' \overline{h} + bch' + eg' h + fgh \)` can be implemented using only 2-to-1 MUXes.

(b) Implementing the same function using only tri-state buffers is not feasible.

Step-by-step explanation:

(a) To implement the given Boolean function
`\( R = ab' \overline{h} + bch' + eg' h + fgh \)` using 2-to-1 MUXes, we can use each MUX to select between two terms in the function. The control inputs of the MUXes can be driven by the input variables and their complements, allowing us to select the appropriate term based on the input values.

(b) However, implementing the same function using only tri-state buffers may not be possible. Tri-state buffers are primarily used for bus-based systems where multiple devices share a common bus. They are not inherently designed for implementing complex Boolean functions directly. The flexibility of MUXes in selecting and combining inputs based on control signals makes them more suitable for such tasks.

Answer 2

To implement the given function using only 2-to-1 MUXes, connect the inputs and outputs as stated. Repeat these steps using tri-state buffers.

Step-by-step explanation:

To implement the given function using only 2-to-1 MUXes, we can use the inputs a,b,c,e,f,g,h as the select inputs and use the inputs ab'h', bch', eg'h', and fgh as the data inputs. The output R can be obtained by connecting the output of each MUX to a common output line. Here is the implementation:

R = (a' AND b' AND h') OR (b AND c AND h') OR (e' AND g AND h) OR (f AND g AND h)

To implement the function using only tri-state buffers, we can use the inputs a,b,c,e,f,g,h as the enable inputs and use the inputs ab'h', bch', eg'h', and fgh as the data inputs. The output R can be obtained by connecting the output of each tri-state buffer to a common output line. Here is the implementation:

R = (ab'h' AND a) OR (bch' AND b) OR (eg'h AND e) OR (fgh AND g)