Page 91 - Computer Science V2.0 Class 11

for no other combination of values of x, y, z. The sum of the three expressions obtained above clearly meets this
requirement. Therefore, F = x'yz' + xy'z + xyz'. Note that each of the three terms in the expression for F is a
product of literals. The expression so obtained for F is called the canonical sum of products or simply the sum of
products.

Let's Summarise

Ø A Boolean variable is also known as binary variable or logical variable that takes its values from the Boolean
algebra.

Ø The values which are stored in binary variables are known as Boolean constants. For example,
true/false,
Ø The two values of a binary signal may be called 1–0, true–false, high–low, etc.
Ø A Truth table is a representation of a Boolean function or expression containing all possible combinations of
input.
Ø Values and their result in a tabular format Boolean operators are operators used in Boolean algebra For
example, AND, OR, NOT, NOR, NAND and XOR.
Ø The AND operator (often called AND gate) is denoted by writing AND, putting a dot, or simply by the absence
of an operator. Thus, A AND B, A ● B, and AB all mean the same.

A B A ● B
0 0 0
0 1 0
1 0 0
1 1 1
Ø The OR operator (often called OR gate) is denoted by writing OR or +.

A B A + B
0 0 0
0 1 1
1 0 1
1 1 1
Ø The NOT operator (often called NOT gate) is denoted by writing NOT before the variable or by putting a bar
over it or by appending a prime (‘). Thus, NOT A, Ā, A' all mean the negation of A.

A NOT A
0 1
1 0
Ø The basic digital circuits (NOT, AND, OR) used to manipulate the digital logic signals are also called logic gates.

Ø The AND gate yields 1 if both the incoming signals are 1, and 0 otherwise.
Ø The OR gate yields 1 if either of the input symbols is 1 and 0 otherwise.
Ø The NOT gate yields 1 if the input signal is 0 and 1 otherwise.
Ø + and ● are also called disjunction and conjunction, respectively.

Boolean Logic 77