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Homework answers / question archive / Homework assignment Digital logic design (CP120), Spring 2021 Dr
Homework assignment
Digital logic design (CP120), Spring 2021
Dr. Heyfa Ammar
Assigned: Tuesday, April 6th, 2021
Due date: Wednesday, April 14th, 2021.
Read Carefully:
• This homework is worth 20% of your final grade. It is composed of two parts. Part1 is mandatory and is worth 10%. Part 2 (out of 10) is not mandatory but your grade obtained in the quiz 1 will be considered instead, if you do not work on Part 2.
• WARNING: This is an individual assignment; you must solve it by yourself. Two identical solutions from two students will be discarded for both and attributed the mark zero.
• moodle Submission:
• This assignment must be submitted online via moodle
• If your file is empty or you upload the wrong file, it will be solely your responsibility, and your mark will be zero.
o Your homework file should be named as:
StudentName_StudentId_HWK.docx
Part1 (Mandatory) (10 marks)
Exercise 1
Consider the following two functions of 5 variables.
F (A, B, C, D, E) = ∑ m (0, 1, 2, 3, 4, 5, 6, 7, 19, 22)
G (A, B, C, D, E) = ∑ m (1, 2, 7, 24, 25, 26, 27, 28, 29, 30, 31)
a. Implement the functions F and G using only 3-input, 8-output, active low decoders, each with one active low enable input and two NAND gates (with as many inputs as are necessary). A truth table and a block diagram of the decoder is shown below.
b. Describe your solution
EN' A1 A2 A3 Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7
1 X X X 1 1 1 1 1 1 1 1
0 0 0 0 0 1 1 1 1 1 1 1
0 0 0 1 1 0 1 1 1 1 1 1
0 0 1 0 1 1 0 1 1 1 1 1
0 0 1 1 1 1 1 0 1 1 1 1
0 1 0 0 1 1 1 1 0 1 1 1
0 1 0 1 1 1 1 1 1 0 1 1
0 1 1 0 1 1 1 1 1 1 0 1
0 1 1 1 1 1 1 1 1 1 1 0
Exercise 2
For each of the following, the minimum sum of products expressions using K-map.
a. f(w,x,y,z)= ∑ m (2,5,7,8,10,12,13,15)
b. g(a,b,c,d)= ∑m(0,6,8,9,10,11,13,14,15)
c. f(a,b,c,d) = ∑m(0,4,5,6,7,8,9,10,11,13,14,15)
d. f(a,b,c,d)= ∑ m (0,1,2,4,6,7,8,9,10,11,12,15)
e. g(a,b,c,d) = ∑ m (0,2,3,5,7,8,10,11,12,13,14,15)
Part 2 (10 marks)
Exercise 1
For the following truth table
x y z f
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
a) Write the function f as a sum of minterms in numeric form (for example,
∑ m (0, ...)
b) Write f as a sum of minterms function in algebraic form (for example,
x' y + ...)
c) Find a minimum sum of products expression of f (2 terms)
Exercise 2
a. Use the K-Map to represent the following function.
f = a' b' c' + a' b + a b d + a b' c' d'
b. Simplify the function f using the K-map. Explain
Exercise 3
For the following function,
f(x, y, z) = ∑ m (3, 4, 5, 7)
a) Show a two-level NAND gate circuit to implement it. (3 gates)
b) Show a two-level NOR gate circuit to implement it. (3 gates)
Exercise 4
For the following 5-variable function, find BOTH minimum sum of product solutions. (5 terms, 16 literals)
Exercise 5
For the following two functions, find a minimum two-level NAND (sum of products) solution (7 gates, 19 inputs). All inputs are available both uncomplemented and complemented. Show the equations, and a circuit.
