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Design a circuit using nand gates that detects the condition

Problem

Design a circuit using NAND gates that detects the "above" condition for two 2-bit values. That is, given two 2-bit variables x and y, F(x,y) = 1 when the unsigned integer value of x is less than the unsigned integer value of y.

i. Give a truth table for the output of the circuit, F.
ii. Find a minimal sum of products for F.
iii. Implement F using PLA.

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