## anonymous one year ago Please help! 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. a) Give a truth table for the output of the circuit, F. b) Find a minimal sum of products for F. c) use either a PLA or PAL.

1. anonymous

okay, so let's write a truth table for our F(x,y) = 1 $$\begin{array}{c|c} x&y&F\\ \hline 00 & 00 & 0 \\ 00 & 01 & 1\\ 00 & 10 & 1 \\ 00 & 11 & 1\\ 01 & 00 & 0\\ 01 & 01 & 0\\ 01 & 10 & 1 \\ 01 & 11 & 1\\ 10 & 00 & 0\\ 10 & 01 & 0\\ 10 & 10 & 0\\ 10 & 11 & 1\\ 11 & 00 & 0\\ 11 & 01 & 0\\ 11 & 10 & 0\\ 11 & 11 & 0 \end{array}$$

2. anonymous

we can write a sum-of-products from the truth table easily (hint: look at all the columns that yield $$F(x,y)=1$$), if we split $$x,y$$ into individual inputs for each bits -- $$x_1, x_2, y_1, y_2$$ so: $$(x_1'x_2'y_1'y_2)+(x_1'x_2'y_1y_2')+(x_1'x_2'y_1y_2)+(x_1'x_2y_1y_2')+(x_1'x_2y_1y_2)+\dots$$ and then minimizing the expression is easy once you have ita ll out