3) (4 points) Three functions are given, using sigma notation.
$Y_1(A,B,C,D) = \sum (0, 1, 7)$
$Y_2(A,B,C,D) = \sum (3, 4, 9, 10)$
$Y_3(A,B,C,D) = \sum (0, 4, 7, 13)$
a. Write each function in canonical SOP form
$Y_1 = \overline{A}\overline{B}\overline{C}\overline{D} + \overline{A}\overline{B}\overline{C}D + \overline{A}BCD$
$Y_2 = \overline{A}\overline{B}CD + \overline{A}B\overline{C}\overline{D} + A\overline{B}\overline{C}D + A\overline{B}C\overline{D}$
$Y_3 = \overline{A}\overline{B}\overline{C}\overline{D} + \overline{A}B\overline{C}\overline{D} + \overline{A}BCD + A\overline{B}CD$
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
A B C D
$Y_1$ $Y_2$ $Y_3$
CMPEN 270 Module 4 Homework Page 3 of 7
$Y_1 = (A,B,C,D) = \sum (0,1,7)$
$0 = 0000 = \overline{A}\overline{B}\overline{C}\overline{D}$
$1 = 0001 = \overline{A}\overline{B}\overline{C}D$
$7 = 0111 = \overline{A}BCD$
$Y_2 = (A,B,C,D) = \sum (3,4,9,10)$
$3 = 0011 = \overline{A}\overline{B}CD$
$4 = 0100 = \overline{A}B\overline{C}\overline{D}$
$9 = 1001 = A\overline{B}\overline{C}D$
$10 = 1010 = A\overline{B}C\overline{D}$
$Y_3 = (A,B,C,D) = \sum (0,4,7,13)$
$0 = 0000 = \overline{A}\overline{B}\overline{C}\overline{D}$
$4 = 0100 = \overline{A}B\overline{C}\overline{D}$
$7 = 0111 = \overline{A}BCD$
$13 = 1101 = A\overline{B}CD$
