After completing the design and fabrication of a digital system, a designer finds that one more…

After completing the design and fabrication of a digital system, a designer finds that one more inverter is required. However, the only spare gates in the system are a-3 input OR, a 2-input AND, and a 2-input XOR. How should the designer realize the inverter function without adding another IC?

How many different 2-variable logic functions F(X,Y) are there? Write a simplified algebraic expression for each of them.

Q129

Any set of logic-gate types that can realize any logic function is called a complete set of logic gates. For example, 2-input AND gates, 2-input OR gates, and inverters are a complete set, because any logic function can be expressed as a sum of products of variables and their complements, and AND and OR gates with any number of inputs can be made from 2-input gates. Do 2-input NAND gates form a complete set of logic gates? Prove your answer.

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