$(4$ points$)$ Three functions are given, using sigma notation.

$Y_1(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(0,1,7)$

$Y_2(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(3,4,9,10)$

$Y_3(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(0,4,7,13)$

a$.$ Write each function in canonical SOP form

$r_1\frac{?}{b}=ar\frac{A}{b}ar\frac{B}{b}ar(C)D\frac{+}{b}ar\frac{A}{b}ar(B)\frac{C}{b}ar(D)\frac{+}{b}ar(A)BCD$

$r_2\frac{?}{b}=ar\frac{A}{b}ar(B)CD\frac{+}{b}ar(A)\frac{B}{b}ar\frac{C}{b}ar(D)\frac{+}{b}ar\frac{A}{b}ar\frac{B}{b}ar(C)D+\frac{A}{b}ar(B)\frac{C}{b}ar(D)$

$r_3\frac{?}{b}=ar\frac{A}{b}ar\frac{B}{b}ar\frac{C}{b}ar(D)\frac{+}{b}ar(A)\frac{B}{b}ar\frac{C}{b}ar(D)\frac{+}{b}ar(A)BCD+A\frac{B}{b}ar(C)D$

b$.$ Make a circuit, using PLA style, that implements the three functions. A partial circuit is given, draw the necessary wires to implement the functions

Module $4$ Homework

Page $3$ of $7$

CMPEN $270$