Page 29 - Computer science 868 Class 12
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0 1 1 0 0 1 0 1 1 1 1
1 0 0 0 0 0 0 1 1 0 1
1 0 1 0 0 0 0 1 1 1 1
1 1 0 1 0 0 0 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
7. Distributive Law
This law states that
• the product of two variables, when added to a third variable, produces the same result as separately adding each
variable with the third variable and multiplying their sums.
• the sum of two variables, when multiplied to a third variable, produces the same result as separately multiplying
each variable with the third variable and adding their products.
The above laws can be expressed algebraically as follows:
A.(B+C) = A.B + A.C
A + B.C = (A+B).(A+C)
The proof of the above expressions using the truth table is as follows:
A B C A.(B+C) A.B+A.C A+B.C (A+B).(A+C)
0 0 0 0 0 0 0
0 0 1 0 0 0 0
0 1 0 0 0 0 0
0 1 1 0 0 1 1
1 0 0 0 0 1 1
1 0 1 1 1 1 1
1 1 0 1 1 1 1
1 1 1 1 1 1 1
8. Absorption Law
This law is a modified Distributive law where a Boolean variable is ‘absorbed’ or eliminated in a Boolean expression,
thus simplifying it.
A B A+B A.(A+B) A.B A+A.B
0 0 0 0 0 0
0 1 1 0 0 0
1 0 1 1 0 1
1 1 1 1 1 1
The law when expressed algebraically is given as:
A.(A+B) = A
A + A.B = A
The proof using the truth table is given here.
9. De Morgan’s Law
This law states that
• the complement of the sum of two Boolean variables is equal to the product of its individual complemented terms.
• the complement of the product of two Boolean variables is equal to the sum of its individual complemented
terms.
27
Boolean Algebra 27

