Page 26 - Computer_Science_F5

Step 1: Write down the Boolean Step 1: Write down the Boolean equation for
equation for each row each row in the truth table whose output
in the truth table whose is 1. B, Aand AB Chapter One: Computer architecture
output is 1. Step 2: To obtain the final Boolean expression,
Step 2: To obtain the final write down the combined Boolean
FOR ONLINE READING ONLY
Boolean expression, equation whose output is one and by
write down the using the OR operator.
combined Boolean X = AB + AB + AB
equations with Step 3: The Boolean expression obtained may
the output one (1) not be in the final form, but it can be
connected by the AND simplified using the laws and rules of
operator and join them Boolean algebra.
with the OR operator. X = AB + AB + AB
Step 3: The Boolean expression X = AB + AB + AB + AB
obtained may not - Idempotent law
be in the final form. X = AB+ AB + AB +AB - Associative law
Therefore, it can be X = (A + A)B + A(B + B) - Distributive law
simplified using the X = 1.B + A.1 - Complementary law
laws and rules of
Boolean algebra. X = B + A - Identity (A.1 = A)
- Commutative law
X = A + B
The following are
examples of writing Example 1.6
Boolean expressions Write the Boolean expression from the following
from the truth table. truth Table 1.8

Table 1.8: Possible combinations of 1 and 0 for
Example 1.5 variable A, B, C, and X

Write the Boolean expression A B C X
from the truth table as shown 0 0 0 0
in Table 1.7 0 0 1 0
0 1 0 0
Table 1.7: Possible combinations 0 1 1 1
of 1 and 0 for variable 1 0 0 0
A, B, and X 1 0 1 1

A B x 1 1 0 0
0 0 0 1 1 1 1
0 1 1 Solution:
1 0 1 Step 1: Write down the Boolean equation for each
1 1 1 row in the truth table whose output is 1.

17
Student’s Book Form Five

Computer Science Form 5.indd 17 23/07/2024 12:32