Page 21 - Computer_Science_F5

Computer Science Boolean algebra is a way of representing and B are at logical 1, then A + B = 1.
the relationship between the inputs and Therefore, the symbol + represents logical
outputs of a logic circuit. A logic circuit addition and not normal binary addition.
operates in two values: 1 and 0. Boolean The logical addition applies to more than
algebra in digital logic circuit differs from one variable, for example, X + Y + Z =
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ordinary mathematical algebra because P; when values of X, Y and Z are logical
a logic circuit involves only two values, values ‘’1’’, the value of P is ‘’1’’.
which are 1 and 0. In contrast, ordinary
mathematics can represent more than two (b) Logical multiplication
values. Boolean 0 and 1 represent the Logical multiplication uses the logical
status of a voltage variable, also known as symbol ‘’.’’ or AND operator. The possible
its logic level, rather than actual numbers. combination of logical multiplication for
A voltage in a digital circuit is at the logic variables A and B and the resulting output
0 or logic 1 level depending on the exact A.B are as follows:
numerical values. 0.0=0, 0.1=0, 1.0 = 0, 1.1 =1. The logical
multiplication represents the same binary
Logic expressions and laws multiplication except for the last entry,
whereby when both entries A and B
Boolean operations are at logical 1, then A.B=1. Therefore,

Boolean algebra has three basic operations: the symbol “.” represents logical
OR, AND, and NOT. The AND and multiplication. The logical multiplication
OR gates are linked with addition and applies for more than one variable; for
multiplication logic operations.
example, X.Y.Z = P when X, Y and Z

(a) Logical addition values are logical values ‘’1’’, the value
Logical addition uses the logical symbol of P is’’1’’.
‘’+’’, which can be placed between any
number of variables, for example, between Basic laws and rules of Boolean
A and B which represent the logical algebra
value of 1 and 0. The logical addition
(+) is represented by the “OR” operator; Laws and rules were invented to help
therefore, the expression A +B reads as simplify the logic expression and, as a
“A” OR “B”. The possible combinations result, minimise the number of logic gates
of logical addition are as follows: needed to construct various logic circuits.
0 + 0 =0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 1. There are different laws of Boolean
algebra. We will discuss commutative,

The logical addition operation represents associative, distributive, identity,
the same binary addition except for the idempotent, annulment, complementary,
last entry, whereby when both entries A and double complementary laws.

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for Advanced Secondary Schools

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