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.