Final answer:
The question involves designing a combinational circuit using a decoder and gates to realize given Boolean functions. It requires decomposing each function, and involves the design of a 3-to-8 decoder and the use of AND and OR gates for implementation.
Step-by-step explanation:
The subject of this question is the design of a combinational circuit using a decoder and external gates based on given Boolean functions.
To design this circuit, first analyze each Boolean function separately:
For F1 = x'yz' + xz, you'll need an AND gate for x'yz', another AND gate for xz, and an OR gate to combine the results.
For F2 = xy'z' + x'y + yz', you will need three AND gates for each product term and an OR gate to combine their outputs.
For F3 = x'y'z' + xy, this requires two AND gates, one for x'y'z' and another for xy, and an OR gate to combine these.
Then, choose an appropriate decoder. Typically, a 3-to-8 decoder would suit this design since you would need to decode three input variables (x, y, z). You would then use the outputs of the decoder to implement the AND functions using external gates and combine them with OR gates as needed.
It's important to simplify the Boolean functions as much as possible to minimize the number of gates needed. For example, in the simplified forms:
F1 = (y + x)z can be implemented with a single AND gate after ORing x and y.
F2 = y'z' + x'y + yz' can be simplified before implementation.
F3 = (x + y)z is similar to F1 and can also be implemented with a basic gate structure.