Download 10th Class Computer Science Notes (Unit-06) for Federal Board (FBISE) Islamabad

Download 10th Class Computer Science Notes (Unit # 06) for Federal Board (FBISE) Islamabad.

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Computer Science Notes for 10th Class / SSC-II (Federal Board, Islamabad)

THEORY

Question: What is Boolean algebra?
Boolean algebra is a mathematical logic. It is presented by George Boole. All electronic switches, devices and circuits must have two states. ON and OFF. Therefore this is also termed as switching algebra. Boolean algebra uses algebraic notation to express logical relationship.
Boolean Constants:
i)            0 if not 1
ii)           1 if not 0
Boolean Variables:
Variables are represented by letters of alphabets having values equal to 0 and 1

Question: What do you understand by the logical operations AND and OR?
AND Operation:
In Boolean Algebra AND operation represents logical multiplication. i.e.
Z = X AND Y = X.Y = XY
We can show it in truth table form as:
X
Y
Z
0
0
0
0
1
0
1
0
0
1
1
1

OR Operation:
In Boolean Algebra AND operation represents logical addition. i.e.
Z = X OR Y = X + Y
We can show it in truth table form as:
X
Y
Z
0
0
0
0
1
1
1
0
1
1
1
1


Question: What is a Truth Table? Construct a Truth Table for AND and NOT of AND operations for the three variables X, Y and Z.
A truth table is a table that shows the result of a Boolean expression for all the possible combinations of the values given to the variables used.
Truth Table for AND Operation:



X
Y
Z = A.B
0
0
0
0
1
1
1
0
1
1
1
1

Truth Table for NOT Operation:


X
Z = X
0
1
1
0


Question: State and Prove the following Laws:
Idempotent Law
a)     A + A = A                  b)     A . A = A
a)
L.H.S                                                          R.H.S
=      A + A                                                A
=      (A + A) . 1
=      (A + A) . (A + A)
=      A + (A . A)
=      A + 0
=      A
b)
L.H.S                                                          R.H.S
=      A . A                                         A
=      A . A + 0
=      A . A + A . A
=      A . (A + A)
=      A . 1
=      A

Involution Law
It states that double complementation has cancellation effect. This can be proved by the method of perfect induction as shown in truth table below:-



A
A
A
0
1
0
1
0
1


Absorption Law

a)     A + (A.B) = A                     b)     A . (A + B) = A

a)
L.H.S                                                          R.H.S
=      A + (A . B)                                         A
=      (A . 1) + (A . B)
=      A . (1 + B)
=      A . 1
=      A
b)
L.H.S                                                          R.H.S
=      A . (A + B)                                         A
=      (A + 1) . (A + B)
=      A + (0 . B)
=      A + 1
=      A



=*=*=*=*=

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