Boolean Algebra & Logic Circuits (Cambridge (CIE) A Level Computer Science): Exam Questions

The truth table for a logic circuit is shown.

Write the Boolean logic expression that corresponds to the given truth table as the sum‑of‑products.

Complete the Karnaugh map (K‑map) for the given truth table.

Draw loop(s) around appropriate group(s) in the K‑map to produce an optimal sum‑of‑products.

Write the Boolean logic expression from your answer to part (c) as the simplified sum‑of‑products.

The diagram shows a logic circuit.

Write the Boolean expression that corresponds to the logic circuit as a sum-of-products.

Complete the Karnaugh map (K-map) for the Boolean expression:

$\overline{A}.\overline{B}.\overline{C}+\overline{A}.\overline{B}.C+A.\overline{B}.\overline{C}+A.\overline{B}.C+A.B.\overline{C}+A.B.C$

(2)

(ii) Draw loop(s) around appropriate group(s) in the K-map to produce an optimal sum-of-products.

(2)

(iii) Write the Boolean expression from your answer to part (c)(ii) as a simplified sum-of-products.

(1)

The diagram shows a logic circuit.

Write the Boolean expression that corresponds to the logic circuit as a sum-of-products.

(i) Complete the Karnaugh map (K-map) for this Boolean expression:

$\overline{A}.\overline{B}.\overline{C}+\overline{A}.B.\overline{C}+\overline{A}.B.C+A.\overline{B}.\overline{C}–+A.B.\overline{C}+A.B.C$

(2)

(ii) Draw loop(s) around appropriate group(s) in the K-map to produce an optimal sum-of-products.

(2)

(iii) Write the Boolean expression from your answer to part c(ii) as a simplified sum-of-products.

(1)

This diagram represents a logic circuit.

Complete the truth table for the given logic circuit.

Simplify the given Boolean expression using Boolean algebra.
Show your working.

This logic circuit represents the Boolean expression: X = $\overline{\mathrm{A}+\mathrm{B}+\mathrm{C}}$

Complete this truth table for the given logic circuit.

Apply De Morgan’s laws to the expression: X = $\overline{\mathrm{A}+\mathrm{B}+\mathrm{C}}$

X = ...................................................................................

Simplify the following expression using Boolean algebra.

Show all the stages in your simplification.

T = X.Y.Z + X.$\overline{\mathrm{Y}.}$Z + «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics»«mover»«mi mathvariant=¨normal¨»X«/mi»«mo»§#175;«/mo»«/mover»«annotation encoding=¨application/vnd.wiris.mtweb-params+json¨»{¨fontFamily¨:¨Times New Roman¨,¨fontSize¨:¨18¨,¨autoformat¨:true,¨toolbar¨:¨«toolbar ref=`general`»«tab ref=`general`»«removeItem ref=`setColor`/»«removeItem ref=`bold`/»«removeItem ref=`italic`/»«removeItem ref=`autoItalic`/»«removeItem ref=`setUnicode`/»«removeItem ref=`mtext` /»«removeItem ref=`rtl`/»«removeItem ref=`forceLigature`/»«removeItem ref=`setFontFamily` /»«removeItem ref=`setFontSize`/»«/tab»«/toolbar»¨}«/annotation»«/semantics»«/math»

This diagram represents a logic circuit.

Simplify the given Boolean expression using Boolean algebra.
Show your working.

Y = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics»«mrow»«mover»«mi mathvariant=¨normal¨»A«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»B«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»C«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»D«/mi»«mo»§#175;«/mo»«/mover»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mover»«mi mathvariant=¨normal¨»A«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»B«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mi mathvariant=¨normal¨»C«/mi»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»D«/mi»«mo»§#175;«/mo»«/mover»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mover»«mi mathvariant=¨normal¨»A«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»C«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»D«/mi»«mo»§#175;«/mo»«/mover»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mover»«mi mathvariant=¨normal¨»A«/mi»«mo»§#175;«/mo»«/mover»«mo».«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo».«/mo»«mi mathvariant=¨normal¨»C«/mi»«mo».«/mo»«mover»«mi mathvariant=¨normal¨»D«/mi»«mo»§#175;«/mo»«/mover»«/mrow»«annotation encoding=¨application/vnd.wiris.mtweb-params+json¨»{¨fontFamily¨:¨Times New Roman¨,¨fontSize¨:¨18¨,¨autoformat¨:true,¨toolbar¨:¨«toolbar ref=`general`»«tab ref=`general`»«removeItem ref=`setColor`/»«removeItem ref=`bold`/»«removeItem ref=`italic`/»«removeItem ref=`autoItalic`/»«removeItem ref=`setUnicode`/»«removeItem ref=`mtext` /»«removeItem ref=`rtl`/»«removeItem ref=`forceLigature`/»«removeItem ref=`setFontFamily` /»«removeItem ref=`setFontSize`/»«/tab»«/toolbar»¨}«/annotation»«/semantics»«/math»