Recent questions tagged boolean-algebra

Which of the following functions represent(s) the output of the CMOS logic-gate shown in the circuit below?$f=\overline{\mathrm{A}}+\overline{\mathrm{B}} \cdot \overline{...

The minimized expression of the Boolean function $\mathrm{Y}(\mathrm{P}, \mathrm{Q}, \mathrm{R})$ implemented by the multiplexer (MUX) circuit shown in the figure is$\mat...

Among the given options, the simplified form of the Boolean function $\mathrm{F=(A+\bar{A} \cdot B)+\bar{A} \cdot(A+\bar{B}) \cdot C}$ is$\mathrm{A+B+C}$$\mathrm{A \cdot ...

Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ is a Boolean input.$$\begin{array}...

The simplified form of the Boolean function $\mathrm{F}(W, X, Y, Z)=\Sigma(4,5,10,11,12,13$, $14,15)$ with the minimum number of terms and smallest number of literals in ...

$A= a_{1}a_{0}$ and $B= b_{1}b_{0}$ are two $2$–bit unsigned binary numbers. If $F(a_{1},a_{0},b_{1},b_{0})$ is a Boolean function such that $F=1$ only when $A>B,$ and $F...

Boolean function $\text{F}$ of three variable $\text{X, Y,}$ and $\text{Z}$ is given as$F\left ( X, Y, Z \right )=\left ( {X}' + Y + Z \right )\cdot \left ( X + {Y}' + {Z...

Given $f(A,B,C,D)=\sum m(0,1,2,6,8,9,10,11)+\sum d(3,7,14,15)$ is a Boolean function, where m represents min-terms and d represents don’t-cares. The minimal sum of produc...

The boolean expression for the shaded regions as shown in the figure is _________$(A+B)\bullet (\overline{A}+\overline{B})$$(A+\overline{B})\bullet (\overline{A}+B)$$(\ov...

The total number of Boolean functions with distinct truth-tables that can be defined over 3 Boolean variables is $\_\_\_\_$.

$X=X_1X_0 \;and\;Y=Y_1Y_0$ are 2-bit binary numbers. The Boolean function $S$ that satisfies the condition “If $X>Y$, then $S=1”$, in its minimized form, is$X_1Y_1+X_0Y_0...

The Boolean expression $XY+(X’+Y’)Z$ is equivalent to$XYZ’+X’Y’Z$$X’Y’Z’+XYZ$$(X+Z)(Y+Z)$$(X’+Z)(Y’+Z)$

In the circuit shown below, $\text{Q}_1$ has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If $\...

In the sum of products function $f(X,\;Y,\;Z)=\sum(2,\;3,\;4,\;5),$ the prime implicants are $\overline{X}Y,\;X\overline{Y}$$\overline{X}Y,\;X\overline{Y}\;\overline{Z},\...

The product of sum expression of a Boolean function F(A, B, C) of three variables is given by$F(A, B, C) = (A + B + \overline{C}) \cdot(A + \overline{B} + \overline{C}) \...