Digital Circuit Systems

Boolean Algebra Viva Questions

Boolean Algebra Viva Questions

Boolean Algebra Viva Questions, Short Questions on Boolean Algebra, Viva Questions on Boolean Algebra, Digital Electronics Viva Questions, Engineering Viva Questions

Binary Codes Viva Questions

Short Questions and Answers

Q.1. What is a literal?

Ans. A logical variable in complemented or uncomplemented form is known as a literal.

Q.2. What is a binary variable?

Ans. The binary variable is a variable that can have only two values 0 and 1.

Q.3. What is switching theory?

Ans. Switching theory is the mathematical theory of logic circuits.

Q.4. What is Boolean algebra?

Ans. Boolean algebra is a system of mathematical logic that uses the letters of the English alphabet to represent variables. Any single variable or a function of the variables can have a value of either 0 or 1.  In Boolean algebra, there is no subtraction or division. Only logical addition and logical multiplication are performed. There are no fractions or negative numbers. It is the algebra of binary variables.

Q.5. What are the basic operations in Boolean algebra?

Ans. The basic operations in Boolean algebra are as follows:

  • AND operation. It is the same as logical multiplication. It is denoted by ‘.’ or ∩ or ˄ or no symbol at all.
  • OR operation. It is the same as logical addition. It is denoted by + or U or ˅.
  • NOT operation. It is the same as inversion or complementation. It is denoted by a bar or prime.

Q.6. What is NAND, NOR, X-OR, and X-NOR operations in Boolean algebra?

Ans. In Boolean algebra, the NAND operation is a combination of AND, and NOT operations. It is a complementation of AND operation. The NOR operation is a combination of OR and NOT operations. It is a complementation of OR operation. The X-OR operation is called the modulo-2 addition operation. The X-NOR operation is a combination of X-OR and NOT operations.

Q.7. What do you mean by an Axim?

Ans. Axims or postulates of Boolean algebra are a set of logical expressions that we accept without proof and upon which we can build a set of useful theorems.

Q.8. State De Morgan’s theorem.

Ans. De Morgan’s theorem states that

  • the complement of a sum of variables is equal to the product of their individual complements and
  • the complement of a product of variables is equal to the sum of their individual complements.

Q.9. What is the use of De Morgan’s theorem?

Ans. De Morgan’s theorem allows the removal of variables under a NOT sign. It allows transformation from SOP form to POS form and vice versa.

Q.10. How do you De Morganize a Boolean expression?

Ans. To De Morganize an expression, complement the entire function, change all the ANDs to ORs, all the ORs to ANDs, 0s to 1s, and 1s to 0s, and then complement each of the individual variables.

Q.11. How do you obtain the dual of an expression?

Ans. The dual of an expression is obtained by changing the ANDs to ORs, ORs to ANDs, 0s to 1s, and 1s to 0s. The variables are not complemented.

Q.12. What does a logical operation in a Boolean expression represent?

Ans. Every logic operation in the Boolean expression represents a corresponding element of hardware.

Q.13. What are the two basic forms of Boolean expressions?

Ans. The two basic forms of Boolean expressions are (a) SOP form and (b) POS form.

Q.14. What is hybrid form?

Ans. The hybrid form of realization is a combination of both SOP and POS forms.

Q.15. What is AOI logic?

Ans. AOI logic is one in which the circuits are realized using AND, OR, and NOT gates only.

Q.16. What is universal logic?

Ans. Universal logic is one in which the circuits are realized using either only NAND gates or only NOR gates.

Q.17. What are expandable gates?

Ans. A/O gates in which an additional variable or a combination of variables can be included in the logic operation are called expandable gates.

Q.18. What do you mean by an n-wide A/O gate?

Ans. A circuit having n AND gates feeding an OR gate is called an n-wide A/O gate.

Q.19. What do you mean by an active-LOW gate?

Ans. Active-LOW gates and circuits are those in which the action represented or initiated by a variable occurs when it is equal to a 0.

Q.20. What do you mean by an active-HIGH gate?

Ans. Active-HIGH gates and circuits are those in which the action represented or initiated by a variable occurs when it is equal to a 1.

Q.21. On logic diagrams, what does a bubble at the input indicate?

Ans. On logic diagrams, an inversion bubble at the point where the input is connected to a gate indicates an active-LOW input.

Q.22. What does an OR gate in a positive logic system become in the negative logic system?

Ans. An OR gate in the positive logic system becomes an AND gate in the negative logic system and vice versa.

Q.23. Write the Boolean algebraic laws.

Ans. The laws of Boolean algebra are:

  • Laws of complementation \bar{0}=1; \bar{1}=0; \bar{\bar{A}}=A

A=0 Only when \bar{A}=1; A = 1 only when \bar{A}=0

  • AND laws 0.0 = 0; 0.1 = 0; 1.0 = 0; 1.1 = 1

A.0=0; A.1=A; A.A=A; A.\bar{A}=0

  • OR laws 0+0=0; 0+1=1; 1+0=1; 1+1=1

A+ 0=A; A+ 1=1; A+A=A; A+\bar{A}=1

  • Commutative laws A + B = B +A; AB = BA
  • Associative laws (A + B) + C = A + (B + C); (AB) . C = A . (BC)
  • Distributive laws A . (B + C) = AB + AC; A + BC = (A + B) . (A + C)
  • Redundant literal rule (RLR) A+\bar{A}B=A+B; A(\bar{A}+B)=AB
  • Idempotence laws A.A = A; A + A = A
  • Absorption laws A + AB = A; A(A + B) = A
  • Consensus Theorem (included factor theorem) AB+\bar{A}C+BC=AB+\bar{A}C
  • Transposition theorem AB+\bar{A}C=(A + C)( \bar{A}+ B)
  • De Morgan’s theorem \bar{A+B}=\bar{A}.\bar{B}; \bar{AB}=\bar{A}+\bar{B})

Q.24. When do you say that a signal is asserted?

Ans. When a signal is in its active state, it is said to be asserted. When it is not in its active state, i.e., when it is inactive, it is said to be unasserted.

Q.25. What do you mean by assertion level?

Ans. The assertion level refers to the signal level necessary to cause an event to occur.

Q.26. What are the merits and demerits of hybrid logic?

Ans. Hybrid logic reduces the number of gate inputs required for realization but results in multi-level logic. Different inputs pass through different numbers of gates to reach the output. It leads to a non-uniform propagation delay between input and output and may give rise to a logic race.

Q.27. What is the advantage of SOP and POS forms of realization?

Ans. The SOP and POS realizations give rise to two-level logic. The two-level logic provides a uniform time delay between input and output because each input signal has to pass through two gates to reach the output. So it does not suffer from the problem of logic race.

Q.28. How do you convert AOI logic to universal logic?

Ans. The procedure to convert AOI logic to universal logic is as follows:

  • Draw the circuit in AOI logic.
  • If NAND hardware is chosen, add a circle at the output of each AND gate and at the inputs to all OR gates.
  • If NOR hardware is chosen, add a circle at the output of each OR gate and at the inputs to all the AND gates.
  • Add or subtract an inverter on each line that received a circle in steps (b) or (c) so that the polarity of signals on those lines remains unchanged from that of the original diagram.
  • Replace bubbled OR by NAND and bubbled AND by NOR.
  • Eliminate double inversions.

Q.29. Why reduce Boolean expressions before realization?

Ans. Every Boolean expression must be reduced to as simple a form as possible before realization because every logic operation in the expression represents a corresponding element of hardware. Realization of a digital circuit with minimal expression, therefore, results in a reduction of cost and complexity and the corresponding increase in reliability.

Q.30. What is the systematic procedure to reduce Boolean expressions?

Ans. The systematic procedure to reduce Boolean expressions is as follows:

  • Multiply all variables necessary to remove parenthesis.
  • Look for identical terms. Only one of those terms be retained and all other terms be dropped.
  • Look for a variable and its negation in the same term. This term can be dropped.
  • Look for pairs of terms that are identical except for one variable which may be missing in one of the terms. The larger term can be dropped.
  • Look for the pairs of terms which have the same variables, with one or more variables complemented in one of those terms. Such terms can be combined into a single term with that variable dropped.

In fact, all the laws of Boolean algebra may be used to reduce the Boolean expression.

Q.31. What are the advantages of minimizing logical expressions?

Ans. The minimization of logic expression leads to savings in cost, space, and power requirements.

Q.32. Which form of a logical expression is suitable for the realization of digital circuits using only (a) NAND gates and (b) NOR gates?

Ans. (a) Only NAND gates – SOP form        (b) only NOR gates – POS form

Q.33. What is AND-OR realization?

Ans. It is a two-level realization employing AND gates at the first level and an OR gate at the second level.

Q.34. What is OR-AND realization?

Ans. It is a two-level realization employing OR gates at the first level and an AND gate at the second level.

 Q.35. Why are NAND-NAND and NOR-NOR realizations preferred over other forms?

Ans. NAND-NAND and NOR-NOR realizations are preferred over other forms because they require only one kind of gate which minimizes IC package count.

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