Submitted to: Mr. Pham Submitted by: Jody Decker Submitted on: 10/08/2007 Performed on: 10/01/2007 Lab Group #1
Jody Decker Elctec 130-001 Lab – Section 4-4 Page 1 of 6 OBJECTIVES 1. Design and build a Majority circuit Using AND & OR gates • Using NAND & NOR gates • 2. Design and build a Minority circuit Using AND, OR & Inverter gates • Using NAND, NOR & Inverter gates • MATERIALS
Quad 2-Input AND gate – 7408 Quad 2-Input OR gate – 7432 Quad 2-Input NAND gate – 7400 Quad 2-Input NOR gate – 7402 Hex Inverter – 7404
• • • • •
PROCEDURES
MAJORITY CIRCUIT 1) Set up truth table so that the output X will be 1 whenever two or more inputs are 1. 2) Write AND term for each case where output is one # 0 1 2 3 4 5 6 7
A 0 0 0 0 1 1
B 0 0 1 1 0 0
C 0 1 0 1 0 1
X 0 0 0 1 0 1
1 1
1 1
0 1
1 1
TERM
A BC
A B C ABC ABC
3) Write sum of products for the output X = A BC + A B C + ABC + ABC
4) Simplify output expression Algebraically X = A BC + A B C + ABC + ABC X = A BC + ABC + A B C + ABC + ABC + ABC X = BC ( A X = AB
•
)
(
+ A + AC B + B
) + AB (C + C )
+ AC + BC
Using K-map method
A BC
ABC
C
C
0
1
A B
00
0
0
A B
01
0
1
AB
11
1
1
A B
10
0
1
A B C
Loop 3 ABC , Loop 6 ABC , Loop 5 ABC = AB + AC + BC BC
AB
AC
Jody Decker Elctec 130-001 Lab – Section 4-4 Page 3 of 6 5) Draw Logic circuit for final expression and construct circuit using AND and OR gates. (AND – 7408, OR – 7432)
6) Redraw Logic circuit using equivalent configurations of NAND, NOR, and Inverter gates as necessary. (NAND – 7400, NOR 7402, Hex Inverter – 7404)
7) Make adjustments to schematic to remove unnecessary logic gates, and to use as few chips as possible to complete circuit.
MINORITY CIRCUIT 1) Set up truth table so that the output X will be 1 whenever two or more inputs are 0. 2) Write AND term for each case where output is one
0
A 0
B 0
C 0
X 1
A B C
1
0
0
1
1
A B C
2
0 0 1 1 1 1
1 1 0 0 1 1
0 1 0 1 0 1
1 0 1 0 0 0
A BC
#
3 4 5 6 7
TERM
A B C
3) Write sum of products for the output X = A B C + A B C + A BC + A B C
4) Simplify output expression Algebraically X = A B C + A B C + A BC + A B C X = A B C + A B C + A B C + A BC + A B C + A B C X = X = A B (C + C ) + A C ( B X = X = A B
•
+ B
) + B C ( A + A)
+ A C + B C
Using K-map method
A B C
A BC
C
C
0
1
A B
00
1
1
A B
01
1
0
AB
11
0
0
A B
10
1
0
A B C
Loop 1 A B C , Loop 2 A B C , Loop 4 A B C = A B A B
A C
B C
+ A C + B C
Jody Decker Elctec 130-001 Lab – Section 4-4 Page 6 of 6 5) Draw Logic circuit for final expression and construct circuit using AND and OR gates. (AND – 7408, OR – 7432)
6) Redraw Logic circuit using equivalent configurations of NAND, NOR, and Inverter gates as necessary. (NAND – 7400, NOR 7402, Hex Inverter – 7404)
7) Make adjustments to schematic to remove unnecessary logic gates, and to use as few chips as possible to complete circuit.
