Exercises 6.4 Exercise
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 \(y\text{.}\)
Give a truth table for the output of the circuit, \(F(x,y)\text{.}\)
Find a minimal sum of products for \(F(x,y)\text{.}\)
Implement \(F(x,y)\) using NAND gates.
Solution
| \(x_1\) | \(x_0\) | \(y_1\) | \(y_0\) | \(F(x,y)\) |
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(0\) | \(0\) | \(1\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(0\) | \(1\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(1\) | \(0\) | \(0\) | \(1\) | \(0\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(0\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(0\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(0\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(0\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) |