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the complement of individual variables Application of DeMorgan’s theorem
connected by OR operator. For two DeMorgan’s theorem can be used to
variables, A and B and three variables, simplify Boolean expression and create
A, B and C, the AND product inverted alternative gates from the basic gates. Chapter One: Computer architecture
theorem can be expressed as follows: The following steps will guide you to
FOR ONLINE READING ONLY
AB = A B+ and ABC = A B C+ + . simplify a Boolean expression using
DeMorgan’s theorem and Boolean
Creating a truth table to prove algebra laws.
DeMorgan’s theorem
The truth table is usually used to prove Example 1.8
different Boolean expressions. The truth Simplify the Boolean expression
table in this section is used to prove
DeMorgan’s theorem. The following A BC+ using DeMorgan’s theorem
examples show the proof of DeMorgan’s and Boolean algebra laws.
theorem using the truth table.
Solution:
Example 1.7 Step 1: Determine the terms you can

Prove DeMorgan’s theorem apply DeMorgan’s theorem
A B+ = . AB , by using truth table. and treat each term as a single
variable. Let x = A BC+ and
Solution: y = BC
Step 1: The expression has two Step 2: Using DeMorgan’s theorem,
variables, A and B. the expression y = BC will
Step 2: Since the expression has two be y = BC+ . Therefore,
variables, A and B; then, the
number of rows are 2 = 4 ABC+ = AB C+ +
2
Step 3: Variables are A and B, and Step 3: Using DeMorgan’s theorem
every possible combination the expression A BC+ + will
of 1 and 0 for each variable be = A ..BC
is as in Table 1.10:
Step 4: Using double negation law,
Table 1.10: Possible combinations for A the expression ..A BC will be
and B A ..BC

A B A B A+B A+ B A.B

0 0 1 1 0 1 1 Example 1.9
0 1 1 0 1 1 1 Simplify the Boolean expression
1 0 0 1 1 1 1 ABC BC+ using DeMorgan’s
1 1 0 0 1 0 0 theorem and Boolean algebra laws.

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Student’s Book Form Five

Computer Science Form 5.indd 19 23/07/2024 12:32