Boolean Algebra

Boolean algebra is mathematics of logic circuits.  Other useful  techniques based on Boolean theorems include the use of Karnaugh maps known as the mapping method and Quine–McCluskey method known as tabular method.

Difference between Boolean Algebra and ordinary algebra
1. In ordinary algebra, the letter symbols take any number of values. In Boolean algebra, they take two values, i.e. 0 and 1.
2. The values assigned to a variable have a numerical significance in ordinary algebra, whereas in Boolean algebra they have a logical significance.
3.  ” . ” and  ” + ” are the signs of multiplication and addition in ordinary algebra. In Boolean algebra ” . ” means an AND operation and ” + ” means OR operation.

Boolean Theorems
Theorem 1:
(a) 0X = 0 and (b) 1+X = 1
Theorem 2:
(a) 1X = X and (b) 0+X = X
Theorem 3:
(a) X . X . X . ………X = X   and (b) X+X+X +···+X = X
Theorem 4:
(a) X . X’ = 0 and (b) X+X’ = 1
Theorem 5:
(a) X+Y = Y +X  and  (b) XY = YX
Theorem 6:
(a) X+Y +Z = Y +Z+X = Z+X+Y  and  (b)  XYZ = YZX = ZXY
Theorem 7:
(a) X(Y +Z) = XY +XZ and (b) X+YZ = (X+Y) . (X+Z)
Theorem 8:
(a) XY +XY’ = X and (b) (X+Y) (X+Y’) = X
Theorem 9:
(a) (X+Y’). Y = XY and (b)  XY’ +Y = X+Y
Theorem 10:
(a) X+XY = X and (b) X. (X+Y) = X
Theorem 11:
(a) ZX+ZX’Y = ZX+ZY  and  (b) (Z+X). (Z+X’+Y) = (Z+X). (Z+Y)
Theorem 12:
(a) X.Y +X’.Z+YZ = X.Y +X’. Z   and
(b) (X+Y). (X’+Z). (Y +Z) = (X+Y). (X’+Z)
Theorem 13:
(a) (X+Y+Z)’ = X’. Y’. Z’ and (b) (X.Y.Z)’ = X’+Y’+Z’
Theorem 14:
(a) XY +X’Z = (X+Z). (X’+Y) and (b) (X+Y). (X’+Z) = XZ+X’Y

 


Boolean Alegbra Quiz

Boolean Algebra

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1. Karnaugh map is used for the purpose of

 
 
 
 

2. In _____ circuit does not need memory.

 
 
 

3. Which of the following are examples of combinational circuit?

 
 
 
 

4. If Y=AC+BC is given expression then A,B and C are called as_____

 
 
 

5. For three combinational circuit ∑m= (1,4,7)= ______.variable

 
 
 
 

6. Which of the following grouping is not possible in K-map?

 
 
 
 

7. Quad eliminates _____variables

 
 
 
 

8. _____ eliminates three variables

 
 
 
 

9. Don’t care condition (X) may be assumed to be _____.

 
 
 
 

10. A+B=B+A; AB=BA represent which laws

 
 
 
 

11. The logic expression (A+B) (+) can be implemented by giving the inputs A and B to a two-input

 
 
 
 

12. The output of a logic gate is 1 when all its inputs are at logic 1, the gate is either

 
 
 
 

13. The output of a logic gate is 1 when all its inputs are at logic 0. The gate is either

 
 
 
 

14. The most suitable gate to check whether the number of 1’s in a digital word is even or odd is

 
 
 
 

15. The number of rows in the truth table of a 4- input gate is,

 
 
 
 

 

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