Alfaisal University - College of Engineering

Electrical Engineering Department

EE 210: Digital Logic Systems
Assignment #2
Spring 2021 - Due Date: March 8, 2021 at 11:59pm (midnight)

Student Name: SOLUTION

Student Number:

I declare that this submission is my own, and that no part of it has been copied from another source except
where properly acknowledged.
Student’s signature:_________________________

Follow the guidelines below in submitting your work.

1. Your homework should have this cover page duly filled out by you.
2. Where possible and applicable, your solution should be typed and printed.
3. Use white, preferably plain, A4-sized paper in your submission.
4. Start a new page for every new problem. However, more than one sub-problem (or short
problems) can be answered on the same sheet.
5. Arrange problems in the order they are assigned. Do not change problem numbers.
6. Show your work in an organized manner. Do not crowd your solution pages.
7. Elaborate on any assumptions made or shortcuts (jumps) taken in your solution.
8. Reference your figures, tables, constants, equations and conversions, used to complete the
problem.

Problem P1 P2 P3 P4 P5 P6 P7 Total
Mark
Maximum 10 10 10 10 10 10 10 70

Evaluator’s initials: _______________

Date: _______________

Course Learning Outcomes (CLO) Problems

Define and identify the elements and requirements of digital logic

CLO1 1-7
systems.
 Alfaisal University - College of Engineering
Electrical Engineering Department
EE 210: Digital Logic Systems
Assignment #2
Spring 2021 - Due Date: March 8, 2021 at 11:59pm (midnight)

Problem 1:

Demonstrate the validity of the following identities by means of truth tables.

a) The distributive law, i.e., 𝑥(𝑦 + 𝑧) = 𝑥𝑦 + 𝑥𝑧

Answer:

xyz x(y + z) xy xz xy + xz

000 0 0 0 0
001 0 0 0 0
010 0 0 0 0
011 0 0 0 0
100 0 0 0 0
101 1 0 1 1
110 1 1 0 1
111 1 1 1 1

b) The associative law: i.e., 𝑥 + (𝑦 + 𝑧) = (𝑥 + 𝑦) + 𝑧

Answer:
xyz x y+z x + (y +z) (x + y) (x + y) + z

000 0 0 0 0 0
001 0 1 1 0 1
010 0 1 1 1 1
011 0 1 1 1 1
100 1 0 1 1 1
101 1 1 1 1 1
110 1 1 1 1 1
111 1 1 1 1 1

Problem 2:

Simplify the following Boolean expression to a minimum number of literals, then draw the logic diagrams of
the circuits that implements both the original and the simplified expressions.

a) 𝐴′ 𝐵′ 𝐶 + 𝐴𝐵′ 𝐶 + 𝐵𝐶

A'B'C + AB'C + BC = B'C + BC = C

b) 𝑥 ′ 𝑦 ′ 𝑧 ′ + 𝑦′𝑧

x'y'z' + y'z = y'(x'z' + z) = y'(x' + z) = x'y' + y'z

Problem 3:
 Alfaisal University - College of Engineering
Electrical Engineering Department
EE 210: Digital Logic Systems
Assignment #2
Spring 2021 - Due Date: March 8, 2021 at 11:59pm (midnight)

Reduce the following Boolean expression to the indicated number of literals

a) (𝐴’ + 𝐶)(𝐴’ + 𝐶’)(𝐴 + 𝐵 + 𝐶’𝐷), reduced to four literals

(A' + C)(A' + C')(A + B + C'D) = (A' + CC')(A + B + C'D) = A'(A + B + C'D) = AA' + A'B + A'C'D
= A'(B + C'D)

b) 𝐴’𝐵𝐷’ + 𝐴𝐵𝐶’𝐷’ + 𝐴𝐵𝐶𝐷’, reduced to two literals

A'BD' + ABC'D' + ABCD' = BD'(A' + AC' + AC) = BD'

Problem 4:

We can perform logical operations on strings of bits by considering each pair of corresponding bits
separately. This is called a bit-wise logical operation.

Given the following two bit strings, A and B, evaluate the eight-bit result of the operations below.

𝐴 = 1011 0001
𝐵 = 0000 1110

a) 𝐴 𝐴𝑁𝐷 𝐵 = 00000000
b) 𝐴 𝑋𝑂𝑅 𝐵 = 10111111
c) 𝑁𝑂𝑇 𝐴 = 01001110
d) 𝐴 𝑁𝑂𝑅 𝐵 = 01000000

Problem 5:

Express the following function as a sum of minterms, and as a product of maxterms

𝐹(𝐴, 𝐵, 𝐶, 𝐷) = 𝐵′ 𝐷 + 𝐴′ 𝐷 + 𝐵𝐷 + 𝐵𝐶𝐷

F(A, B, C, D) = B'D + A'D + BD+ BCD

=_0_1+0__1+_B_D+_BCD

_ 0 _ 1 → 0001(1), 0011(3), 1001(9), 1011(11)

0 _ _1 → 0001(1), 0011(3), 0101(5), 0111(7)
_ 1 _ 1 → 0101(5), 0111(7), 1101(13), 1111(15)
_1 1 1 → 0111(7), 1111(15)
=  (1, 3, 5, 7, 9, 11,13, 15)
=  (0, 2, 4, 6, 8, 10, 12, 14)
 Alfaisal University - College of Engineering
Electrical Engineering Department
EE 210: Digital Logic Systems
Assignment #2
Spring 2021 - Due Date: March 8, 2021 at 11:59pm (midnight)

Problem 6:

Convert the following expression into the other canonical form

𝐹(𝐴, 𝐵, 𝐶, 𝐷) = Π(3, 5, 8, 11, 13, 15)

F (A, B, C, D) = (3, 5, 8, 11, 13, 15) = (0, 1, 2, 4, 6, 7, 9, 10, 12, 14)

Problem 7:

Convert the following expression into a sum of products and a product of sums

𝑥′ + 𝑧(𝑥 + 𝑦 ′ )(𝑦 + 𝑧 ′ )

x' + z (x + y') (y + z')

= x' + (xz + zy') (y + z')

= x' + xzy + xz z' + zy'y + zy' z'

= x' + xyz + x.0 + z.0 + y'.0

= x' + xyz [hint: a' + ab = a' + b]

= x' + yz → SOP form
[hint: a + bc = (a + b) (a + c)]
= (x' + y) (x' + z) → POS form