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Boolean Algebra and Logic Simplification problems

  • 1. How many gates would be required to implement the following Boolean expression after simplification? XY + X(X + Z) + Y(X + Z)

  • Options
  • A. 1
  • B. 2
  • C. 4
  • D. 5
    • Discuss
  • 2. The commutative law of Boolean addition states that A + B = A × B.

  • Options
  • A. True
  • B. False
    • Discuss
  • 3. Determine the values of A, B, C, and D that make the sum term Digital Electronics Boolean Algebra and Logic Simplification: Determine the values of A, B, C, and D that make the sum term equal to zero.

  • Options
  • A. A = 1, B = 0, C = 0, D = 0
  • B. A = 1, B = 0, C = 1, D = 0
  • C. A = 0, B = 1, C = 0, D = 0
  • D. A = 1, B = 0, C = 1, D = 1
    • Discuss
  • 4. A Karnaugh map is a systematic way of reducing which type of expression?

  • Options
  • A. product-of-sums
  • B. exclusive NOR
  • C. sum-of-products
  • D. those with overbars
    • Discuss
  • 5. The Boolean expression Digital Electronics Boolean Algebra and Logic Simplification: The Boolean expression is logically equivalent to what single gate?

  • Options
  • A. NAND
  • B. NOR
  • C. AND
  • D. OR
    • Discuss
  • 6. Applying DeMorgan's theorem to the expression Digital Electronics Boolean Algebra and Logic Simplification: Applying DeMorgan's theorem to the expression, we get ________

  • Options
  • A.
  • B.
  • C.
  • D.
    • Discuss
  • 7. Which of the following is an important feature of the sum-of-products (SOP) form of expression?

  • Options
  • A. All logic circuits are reduced to nothing more than simple AND and OR gates.
  • B. The delay times are greatly reduced over other forms.
  • C. No signal must pass through more than two gates, not including inverters.
  • D. The maximum number of gates that any signal must pass through is reduced by a factor of two.
    • Discuss
  • 8. Which Boolean algebra property allows us to group operands in an expression in any order without affecting the results of the operation [for example, A + B = B + A]?

  • Options
  • A. associative
  • B. commutative
  • C. Boolean
  • D. distributive
    • Discuss
  • 9. Derive the Boolean expression for the logic circuit shown below:

    Digital Electronics Boolean Algebra and Logic Simplification: Derive the Boolean expression for the logic circuit shown below:


  • Options
  • A.
  • B.
  • C.
  • D.
    • Discuss
  • 10. An AND gate with schematic "bubbles" on its inputs performs the same function as a(n)________ gate.

  • Options
  • A. NOT
  • B. OR
  • C. NOR
  • D. NAND
    • Discuss

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