Question 1 |
Select the Boolean function(s) equivalent to x+yz, where x,y, and z are Boolean
variables, and + denotes logical OR operation.
x+z+xy | |
(x+y)(x+z) | |
x+xy+yz | |
x+xz+xy |
Question 1 Explanation:
A. x + z + xy = x(1 + y) + z = x + z
B. (x + y) (x + z) = x + xz + xy + yz = x(1 + y + z) + yz = x + yz
C. x + xy + yz = x(1+y) + yz = x + yz
D. x + xz + xy = x (1 + z + y) = x
B. (x + y) (x + z) = x + xz + xy + yz = x(1 + y + z) + yz = x + yz
C. x + xy + yz = x(1+y) + yz = x + yz
D. x + xz + xy = x (1 + z + y) = x
Question 2 |
A function F(A,B,C) defined by three Boolean variables A, B and C when expressed as sum
of products is given by
F=\bar{A}\cdot \bar{B} \cdot \bar{C} + \bar{A}\cdot B \cdot \bar{C} + A\cdot \bar{B} \cdot \bar{C}
where,\bar{A},\bar{B} \;and \; \bar{C} are complements of the respective variable. The product of sums (POS) form of the function F is
F=\bar{A}\cdot \bar{B} \cdot \bar{C} + \bar{A}\cdot B \cdot \bar{C} + A\cdot \bar{B} \cdot \bar{C}
where,\bar{A},\bar{B} \;and \; \bar{C} are complements of the respective variable. The product of sums (POS) form of the function F is
F=(A+B+C)\cdot (A+\tilde{B}+C)\cdot (\bar{A}+B+C) | |
F=(\bar{A}+\bar{B}+\bar{C})\cdot (\bar{A}+B+\bar{C})\cdot (A+\bar{B}+\bar{C}) | |
F=(A + B + \bar{C}) \cdot (A + \bar{B} + \bar{C} ) \cdot (\bar{A} + B + \bar{C}) \cdot (\bar{A}+\bar{B}+C) \cdot (\bar{A}+\bar{B}+\bar{C}) | |
F=(\bar{A} + \bar{B} + C) \cdot (\bar{A} + B + C) \cdot (A + B + \bar{C}) \cdot (A+B+C) |
Question 2 Explanation:
\begin{aligned} F(A, B, C, D) &=\bar{A} \bar{B} \bar{C}+\bar{A} B \bar{C}+A \bar{B} \bar{C} \\ &=\Sigma m(0,2,4)=\Pi M(1,3,5,6,7) \\ =&(A+B+\bar{C})(A+\bar{B}+\bar{C})(\bar{A}+B+\bar{C}) \\ &(\bar{A}+\bar{B}+C)(\bar{A}+\bar{B}+\bar{C}) & \end{aligned}
Question 3 |
Which one of the following gives the simplified sum of products expression for the Boolean function F=m_{0}+m_{2}+m_{3}+m_{5}, where m_{0},m_{2},m_{3},m_{5}, are minterms corresponding to
the inputs A, B and C with A as the MSB and C as the LSB?
\bar{A}B+\bar{A}\bar{B}\bar{C}+A\bar{B}C | |
\bar{A}\bar{C}+\bar{A}B+A\bar{B}C | |
\bar{A}\bar{C}+A\bar{B}+A\bar{B}C | |
\bar{A}BC+\bar{A}\bar{C}+A\bar{B}C |
Question 3 Explanation:
Given Boolean function is,
F=m_{0}+m_{2}+m_{3}+m_{5}
It can be minimized by using K-map as given below.
F=\bar{A} \bar{C}+\bar{A} B+A \bar{B} C
F=m_{0}+m_{2}+m_{3}+m_{5}
It can be minimized by using K-map as given below.
F=\bar{A} \bar{C}+\bar{A} B+A \bar{B} C
Question 4 |
Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is
\bar{P}\bar{Q}S\bar{X}+P\bar{Q}S\bar{X}+Q\bar{R}\bar{S}X+QR\bar{S}X | |
\bar{Q}S\bar{X}+Q\bar{S}X | |
\bar{Q}SX+Q\bar{S}\bar{X} | |
\bar{Q}S+Q\bar{S} |
Question 4 Explanation:
\therefore minimum sum of product expression of the function is
=\bar{Q}S\bar{X}+Q\bar{S}X
Question 5 |
A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X,Y,Z)=\sum (1,2,5,6,7)
Which one of the product of sums given below is equal to the function F(X,Y,Z)?
F(X,Y,Z)=\sum (1,2,5,6,7)
Which one of the product of sums given below is equal to the function F(X,Y,Z)?
(\bar{X}+\bar{Y}+\bar{Z})\cdot (\bar{X}+Y+Z)\cdot (X+\bar{Y}+\bar{Z}) | |
(X+Y+Z)\cdot (X+ \bar{Y}+\bar{Z})\cdot (\bar{X}+Y+Z) | |
(\bar{X}+\bar{Y}+Z)\cdot (\bar{X}+Y+\bar{Z})\cdot (X+\bar{Y}+Z) \cdot (X+Y+\bar{Z})\cdot (X+Y+Z) | |
(X+Y+\bar{Z})\cdot (\bar{X}+Y+Z)\cdot (\bar{X}+Y+\bar{Z}) \cdot (\bar{X}+\bar{Y}+Z)\cdot (\bar{X}+\bar{Y}+\bar{Z}) |
Question 5 Explanation:
\begin{aligned} F(X, Y, Z) &=\Sigma(1,2,5,6,7) \\ &=\pi[0,3,4] \\ =(X+Y+Z)&(X+\bar{Y}+\bar{Z})(\bar{X}+Y+Z) \end{aligned}
There are 5 questions to complete.