Page 22 - Computer_Science_F5

However, Boolean algebra laws such as (f) Annulment law
commutative, associative, and distributive Annulment law applies when a variable
are all the same as ordinary algebra. OR with 1 equals 1 or AND with 0 gives
0 as follows: A.0 =0 and A+1=1 Chapter One: Computer architecture
(a) Commutative law
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The commutative law used in Boolean (g) Complementary law
algebra is the same as ordinary algebra. Complementary law applies when a
The addition and multiplication in variable AND with its complement is
commutative laws using two variables 0 and when OR with its complement
are as follows: result is 1.
A+B = B+A and A.B =B.A. Ā.A=0 and Ā+A =1

(b) Associative law (h) Double complementary law

The associative law used in Boolean The double negation law applies when
algebra is the same as ordinary algebra. a variable is inverted twice. Its output is
The addition and multiplication in the same variable .A=A
associative laws using three variables
are as follows: Boolean algebra expression and
(A+B) +C = A+(B+C) and (A.B).C = simplification
A.(B.C).
Boolean algebra operations are the core
of this simplification of logic circuits.
(c) Distributive law The simplification of Boolean expressions
The distributive law used in Boolean reduces the number of logic gates required
algebra is like ordinary algebra. The to implement the logic circuit. There are
addition and multiplication in distributive several reasons one might want to simplify
laws using three variables are as follows: a logic circuit. In modern circuits the
(A+B).C = (A.C)+(B.C) and A+ (B.C) = most common reason is to reduce power
(A +B).(A+C) consumption and/or reduce the amount

of heat the circuit generates. This can
(d) Identity law be important in portable devices and at
The identity law used in Boolean algebra higher levels of hardware design because
is used as follows: power consumption eventually becomes
A+0 = A and A.1 = A a limiting factor.

(e) Idempotent law Boolean algebra expression

This law applies a variable OR or AND Boolean expressions are algebraic
by itself. The output is always the same statements that use variables and logical
variable as follows: operators, such as AND, OR, XOR, and
A+A=A and A.A= A. NOT.

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Student’s Book Form Five

Computer Science Form 5.indd 13 23/07/2024 12:32