Summative Assessment#2

IT2623

Ryle Ibañez 3/07/2022

2ITB Mrs. Maria Lourdes Edang

1. A certain Jose Velarde owns binary slot machine at CASINO FILIPINO. The slot machine is
composed of 4 slots. The jackpot is won whenever 3 adjacent slots consisting of alternating 0's
and l's come up. Determine the equation of this slot machine used to award the jackpot.
Simplify the function and implement it using NAND gates only.

Truth Table

A B C D S
0 0 0 0 0
0 0 0 1 0
0 0 1 0 1
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 0
1 1 0 1 1
1 1 1 0 0
1 1 1 1 0
 K-MAP

SOP

Circuit Diagram

S = B’CD’ + A’BC’ + BC’D + AB’C

Truth Table

A B C D S
0 0 0 0 0
0 0 0 1 0
0 0 1 0 1
0 0 1 1 1
0 1 0 0 1
0 1 0 1 0
0 1 1 0 1
0 1 1 1 0
1 0 0 0 1
1 0 0 1 1
1 0 1 0 1
1 0 1 1 0
1 1 0 0 1
1 1 0 1 0
1 1 1 0 1
1 1 1 1 1

K-MAP

POS
 Circuit Diagram

S = (A’+B+C’+D’)(A+B+C)(A+B’+D’)(B’+C+D’)

3. Simplify the following Boolean function F together with the don't care condition d. Construct the
circuit using NOR-NOR, NOR-AND, and OR-AND networks.

A. F(A,B,C,D) = Σ (0,6,8,14)| D = (A,B,C,D) = Σ(2,4,10)

TRUTH TABLE

A B C D F
0 0 0 0 1
0 0 0 1 0
0 0 1 0 X
0 0 1 1 0
0 1 0 0 X
0 1 0 1 0
0 1 1 0 1
0 1 1 1 0
1 0 0 0 1
 1 0 0 1 0
1 0 1 0 X
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 1
1 1 1 1 0

K-MAP

POS

F = (B’+C)(D’)

LOGIC CIRCUITS

A. NOR-NOR
B. NOR-AND

C. OR – AND
B. F(w,x,y,z) = Σ (0,1,2,3,7,8,10) | D = (w,x,y,z) = Σ(5,6,11,15)

Truth Table

W X Y Z F
0 0 0 0 1
0 0 0 1 1
0 0 1 0 1
0 0 1 1 1
0 1 0 0 0
0 1 0 1 X
0 1 1 0 X
0 1 1 1 1
1 0 0 0 1
1 0 0 1 0
1 0 1 0 1
1 0 1 1 X
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 X

K-MAP

POS

F = (W’+Z’)(X’+Z)
 LOGIC CIRCUITS

1. NOR-NOR

2. NOR-AND
 3. OR-AND

4. Simplify the following Boolean function F together with the don’t care condition d. Construct the
circuit using AND-OR, NAND-OR, and NAND-NAND networks.

a. F(A, B, C, D) = Σ(1, 3, 5, 7, 9, 15); d(A, B, C, D) = Σ(4, 6, 13)

Truth Table

A B C D F
0 0 0 0 0
0 0 0 1 1
0 0 1 0 0
0 0 1 1 1
0 1 0 0 X
0 1 0 1 1
0 1 1 0 X
0 1 1 1 1
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 X
1 1 1 0 0
1 1 1 1 1
 K-MAP

F = A’D + C’D + BD

LOGIC CIRCUIT

A. NAND-NAND

F
A. AND-OR

B. NAND-OR

F
b. F(A, B, C, D) = Σ(3, 4, 13, 15)

Truth Table

A B C D F
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 1
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 1
1 1 1 0 0
1 1 1 1 1

K-MAP

F = A’BC’D’ + A’B’CD + ABD

B. AND-OR

F
C. NAND-OR