Page 27 - Computer_Science_F5

Computer Science down the combined Boolean equations 3. Given the truth Table
ABC, ABC and ABC.
1.9, determine the
Step 2: To obtain the final Boolean expression, write
Boolean expression for
Y in terms of A and B.
whose output is one and OR together.
FOR ONLINE READING ONLY
X = ABC + ABC + ABC
Table 1.9: The truth table

for A,B, and Y
Step 3: The Boolean expression obtained may not
be in the final form. It can be simplified A B Y
using the laws and rules of Boolean algebra. 0 0 0
0 1 1
X = ABC + ABC + ABC
1 0 1
X = ABC + ABC + ABC + ABC - Idempotent law 1 1 0

X=ABC + ABC + ABC + ABC - Commutative law
X = (A + A)BC + AC(B + B)AC - Distributive law DeMorgan’s theorem
X=1.BC+1.AC - Complementary law There are two DeMorgan’s
X=BC + AC - Identity (A.1 = A)
theorems. These are OR sum
X =C(B+A) - Associative law inverted theorem and AND

product inverted theorem.
The OR sum inverted version
Activity 1.8:
of DeMorgan’s theorem
Designing a car safety buzzer circuit states that the complement of

As an electronic engineer, you are tasked with two or more variables joined
designing a car safety buzzer circuit. Here are the by the OR operator is equal to
design specifications: The buzzer should be ON the complement of individual
when the door is OPEN or when the key is in the variables connected by the
IGNITION, and the seat belt is NOT BUCKLED. AND operator. For two
Create a truth table to outline these specifications variables, A and B, and
using “highs” (1) and “lows” (0) to indicate sensor three variables, A, B and
or indicator activity. C, the OR sum inverted
theorem can be expressed
Exercise 1.3 as follows: A B+ = . AB and
..BC The AND
=
+
A
A B C+
.
1. Prove the following using the truth table. product inverted version of
(a) AB + AC + ABC = AB + AC DeMorgan’s theorem states
(b) A + (B + C) = (A + B) + C that the complement of two
2. Create the truth table of the following expression: or more variables joined by
X = A + BC AND operator is equal to

18
for Advanced Secondary Schools

Computer Science Form 5.indd 18 23/07/2024 12:32