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Section6.4Exercise

1

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

  1. Give a truth table for the output of the circuit, \(F(x,y)\text{.}\)

  2. Find a minimal sum of products for \(F(x,y)\text{.}\)

  3. Implement \(F(x,y)\) using NAND gates.

Solution
\(x_1\) \(x_0\) \(y_1\) \(y_0\) \(F(x,y)\)
\(0\) \(0\) \(0\) \(0\) \(0\)
\(0\) \(0\) \(0\) \(1\) \(1\)
\(0\) \(0\) \(1\) \(0\) \(1\)
\(0\) \(0\) \(1\) \(1\) \(1\)
\(0\) \(1\) \(0\) \(0\) \(0\)
\(0\) \(1\) \(0\) \(1\) \(0\)
\(0\) \(1\) \(1\) \(0\) \(1\)
\(0\) \(1\) \(1\) \(1\) \(1\)
\(1\) \(0\) \(0\) \(0\) \(0\)
\(1\) \(0\) \(0\) \(1\) \(0\)
\(1\) \(0\) \(1\) \(0\) \(0\)
\(1\) \(0\) \(1\) \(1\) \(1\)
\(1\) \(1\) \(0\) \(0\) \(0\)
\(1\) \(1\) \(0\) \(1\) \(0\)
\(1\) \(1\) \(1\) \(0\) \(0\)
\(1\) \(1\) \(1\) \(1\) \(0\)

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