
## 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
 $x_1$ $x_0$ $y_1$ $y_0$ $F(x,y)$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $1$ $1$ $0$ $0$ $1$ $0$ $1$ $0$ $0$ $1$ $1$ $1$ $0$ $1$ $0$ $0$ $0$ $0$ $1$ $0$ $1$ $0$ $0$ $1$ $1$ $0$ $1$ $0$ $1$ $1$ $1$ $1$ $1$ $0$ $0$ $0$ $0$ $1$ $0$ $0$ $1$ $0$ $1$ $0$ $1$ $0$ $0$ $1$ $0$ $1$ $1$ $1$ $1$ $1$ $0$ $0$ $0$ $1$ $1$ $0$ $1$ $0$ $1$ $1$ $1$ $0$ $0$ $1$ $1$ $1$ $1$ $0$