# Boolean Algebra – Exercise – 1

Exercise – 1

1. In a digital control system, there are three inputs a,b,c. The output should be present when at least two inputs are present.
The Boolean expression for the output is :

(a)  $\dpi{100} ab+bc+ac$
(b)  $\dpi{100} abc+ab\bar{c}+\bar{a}bc+a\bar{b}c$
(c)  $\dpi{100} b\bar{c}+a\bar{b}c+\bar{a}bc$
(d)  $\dpi{100} a\bar{b}+b\bar{c}+\bar{a}c$

Explanation
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2. Simplified form of :

$\dpi{300} \dpi{80} (X+Y) (X+\bar{Y})$

(a)  $\dpi{80} \dpi{80} X$
(b)  $\dpi{80} Y$
(c)  $\dpi{80} X+X\bar{Y}$
(d)  $\dpi{80} X(1+Y)$

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3. Two binary signals a,b are to be compared. The output expression when the two signals are equal is given by :

(a)  $\dpi{100} a\bar{b}+\bar{a}b$
(b)  $\dpi{100} ab+\bar{a}\bar{b}$
(c)  $\dpi{80} \dpi{100} ab$
(d) $\dpi{100} \bar{a}\bar{b}$

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4. The Boolean expression for the sub-class(R) of all digital electronics instruments which are not measuring instruments and have no battery supply is :

(a)  $\dpi{80} R+X+YZ$
(b)  $\dpi{80} R=XY+Z$
(c)  $\dpi{80} R=\bar{X}\bar{Y}\bar{Z}$
(d)  $\dpi{80} R=XYZ$

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5. The minimum Boolean expression for the circuit shown below :

(a)  XY+XZ+YZ
(b)  X+YZ
(c)  X+Y
(d) X+Y+Z
Explanation
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