Boolean Algebra & K-map

One or more correct

• A$\overline{P \oplus Q}$
• B$P \oplus Q$
• C$\bar{P} \oplus Q$
• D$\bar{P} \oplus \bar{Q}$

One or more correct

• A$\bar{P}S + Q\bar{R} + \bar{P}\bar{Q}R + \bar{Q}R\bar{S}$
• B$\bar{P}S + Q\bar{R} + \bar{P}\bar{Q}R + PR\bar{S}$
• C$\bar{P}S + Q\bar{R} + PQ\bar{S} + PR\bar{S}$
• D$\bar{P}S + Q\bar{R} + PQ\bar{S} + \bar{Q}R\bar{S}$

Single correct

• A$X + Y = Y + X$
• B$X \cdot X' = 1$
• C$X + X' = 1$
• D$X \cdot Y = Y \cdot X$

Single correct

• A$A' + B' + C' + D'$
• B$B'$
• C$A'.B' + A.B$
• D$A'$

One or more correct

• A$X(a, b, X(c, d, e)) = X(X(a, b, c), d, e)$
• B$X(a, b, X(a, b, c)) = X(a, b, c)$
• C$X(a, b, X(a, c, d)) = (X(a, b, a) \text{ AND } X(c, d, c))$
• D$X(a, b, c) = X(a, X(a, b, c), X(a, c, c))$

Single correct

• A$\bar{b}_1\bar{b}_0 + \bar{b}_2\bar{b}_0 + b_1\bar{b}_2b_3$
• B$\bar{b}_1\bar{b}_0 + \bar{b}_2\bar{b}_0$
• C$\bar{b}_2\bar{b}_0 + b_1b_2b_3$
• D$\bar{b}_0\bar{b}_2 + \bar{b}_3$

One or more correct

• A$\overline{XY}$
• B$\bar{X} + \bar{Y} + X\bar{Y}$
• C$\overline{XY} + \bar{X} + X\bar{Y}$
• D$X + \bar{Y}$

One or more correct

• A$\bar{w}\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}\bar{z} + \bar{w}\bar{x}y\bar{z} + w\bar{x}y\bar{z} + xz$
• B$\bar{w}\bar{x}\bar{y}\bar{z} + \bar{w}\bar{x}y\bar{z} + w\bar{x}yz + xz$
• C$\bar{w}\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}z + xz$
• D$\bar{x}\bar{z} + xz$

One or more correct

• A$\bar{A}BC + A\bar{B}\bar{C} + \bar{A}\bar{B}\bar{C} + A\bar{B}C + ABC = BC + \bar{B}\bar{C} + \bar{A}\bar{B}$
• B$AB + \bar{A}C + BC = AB + \bar{A}C$
• C$(A + C)(\bar{A} + B) = AB + \bar{A}C$
• D$\overline{(A + \bar{B} + \bar{D})(C + D)(\bar{A} + C + D)(A + B + \bar{D})} = \bar{A}D + \bar{C}\bar{D}$

One or more correct

• A$F(X, Y, Z) = \Pi(0, 1, 2, 4)$
• B$F(X, Y, Z) = XY + YZ + XZ$
• C$F(X, Y, Z)$ is independent of input $Y$
• D$F(X, Y, Z)$ is independent of input $X$

One or more correct

• A$x \cdot 1 = x$
• B$x + 1 = x$
• C$x \cdot x = 0$
• D$x + \bar{x} = 1$

One or more correct

• A$Y = \sum(0,1,2,11,13)$
• B$Y = \Pi(3,4,5,6,7,8,9,10,12,14,15)$
• C$Y = \sum(0,1,2,3,4,5,6,7)$
• D$Y = \Pi(8,9,10,11,12,13,14,15)$

One or more correct

• A$(\overline{X} + \overline{Y} + \overline{Z})(X + \overline{Y})(Y + \overline{Z})$
• B$X\overline{Y} + \overline{Z}$
• C$(X + \overline{Z})(\overline{Y} + \overline{Z})$
• D$X\overline{Y} + Y\overline{Z} + \overline{X}\,\overline{Y}\,\overline{Z}$

Answer key coming soon

Single correct

• ACircuit (A) in the figure
• BCircuit (B) in the figure
• CCircuit (C) in the figure
• DCircuit (D) in the figure

Answer key coming soon

Numerical answer

Answer key coming soon

Single correct

• A$z = \sum(0, 1, 3, 7)$
• B$z = \sum(1, 4, 5, 6, 7)$
• C$z = \sum(2, 4, 5, 6, 7)$
• D$z = \sum(2, 3, 5)$

Answer key coming soon

Single correct

• A$(x \oplus y) \oplus z = x \oplus (y \oplus z)$
• B$(x + y) \oplus z = x \oplus (y + z)$
• C$x \oplus y = x + y$, if $xy = 0$
• D$x \oplus y = (xy + x'y')'$

Single correct

• A$\Sigma(7, 8, 11)$
• B$\Sigma(2, 7, 8, 11, 14)$
• C$\Sigma(2, 14)$
• D$\Sigma(0, 2, 3, 5, 6, 7, 8, 11, 14, 15)$

Numerical answer

Single correct

• A$\overline{P \oplus Q} = P \odot Q$
• B$\overline{P} \oplus Q = P \odot Q$
• C$\overline{P} \oplus \overline{Q} = P \oplus Q$
• D$(P \oplus \overline{P}) \oplus Q = (P \odot \overline{P}) \odot \overline{Q}$