CANONICAL AND STANDARD FORMS

Question 1

When is an expression said to be SOP or DNF

Answer 1

When the expression of f is of the form:

f = A + BC + DEF

it is called a Sum of Products, or Disjunctive Normal Form (DNF).

Question 1

When is an expression said to be POS or CNF

Answer 1

When the expression of f is of the form:

f = (A) . (B + D) . (D + E + F)

it is called a Product of Sums, or Conjunctive Normal Form (CNF).

Question 2

What is a minterm

Answer 2

a product term in which all the variables appear exactly once, either complemented or
uncomplemented. Denoted by mj

Question 3

What is maxterm?

Answer 3

a sum term in which all the variables appear exactly once, either complemented or uncomplemented. Denoted by Mj

Question 4

What is canonical form

Answer 4

Boolean functions expressed as a sum of
Minterms or product of Maxterms are said to be in
canonical form.

Question 5

Express the boolean function F= A+B’C as a sum of minterms
Express the boolean function F= xy+x’z as product of minterms

Answer 5

*See notes

Question 6

Express the Truth Table notation for Minterms and Maxterms

Answer 6

*See notes

Question 7

What is the standard form?

Answer 7

POS or SOP
Eg AB +C(D+E)- Non-standard
But AB + CD + CE- Standard

Question 8

What is an integrated circuit

Answer 8

an electronic circuit fabricated on a die of a silicon semiconductor crystal, which contains electronic components for constructing digital gates.

Question 8

What is an integrated circuit

Answer 8

an electronic circuit fabricated on a die of a silicon semiconductor crystal, which contains electronic components for constructing digital gates.

Question 9

Describe each level of integration and give examples of their implementations

Answer 9

Small‐scale integration (SSI)
 Several independent gates in a single package.
 Inputs and outputs of the gates are connected directly to the pins in the package. The number of gates = fewer than 10

Medium‐scale integration (MSI)
 Approximately 10 to 1,000 gates in a single package.
 Perform specific elementary digital operations.
 E.g. decoders, adders, and multiplexers, registers and counters.

Large‐scale integration (LSI)
 Contain thousands of gates in a single package.
 E.g. processors, memory chips, and programmable logic devices.

Very large‐scale integration (VLSI)
 Contain millions of gates within a single package.
 E.g. large memory arrays and complex microcomputer chips.