Logic Minimisation

Question 1

Name the ways that cost can be evaluated in combinational logic.

Answer 1

Number of IC packages
Number of gates
Silicon area (VLSI design)
Propagation delay

Question 2

What is the effect of minimising the number of gates in a combinational logic function?

Answer 2

Reduces cost

Question 3

How can we minimise the number of gates in a logic function?

Answer 3

1. By minimising the number of first-level gates
2. By minimising the number of inputs on each first-level gate.
3. By minimising the number of inputs on the second-level gate. This is actually a side effect of the first reduction.

Question 4

What is the name for a boolean function expressed in the form, F = A’BC + AC

Answer 4

Canonical form

Question 5

What is SOP?

Answer 5

Sum of Products - form of representation of a boolean expression involving minterms

Question 6

What is POS?

Answer 6

Product of Sums - Technique of generating a boolean expression involving maxterms

Question 7

What is the order of implementation for a SOP?

Answer 7

OR gate is employed after the AND gate

Question 8

What is the order of implementation for a POS?

Answer 8

1. OR gate - sum terms

2. AND gate - gives product

Question 9

What is the gate equivalent of summing two logic values?

Answer 9

OR gate

Question 10

What is the gate equivalent of multiplying two values?

Answer 10

AND gate

Question 11

How is the SOP obtained?

Answer 11

By adding corresponding product terms

Question 12

How is the POS obtained?

Answer 12

Multiplying the relevant sum terms

Question 13

What is combinational logic?

Answer 13

Logic in which the outputs depend only on current inputs

Question 14

What is a prime implicant?

Answer 14

A group of adjacent 1’s (minterms) in a K-map

Question 15

What are essential prime implicants?

Answer 15

There are subgroups which cover at least one minterm that can’t be covered by another (do not overlap). They always appear in the final solution.

Question 16

What is a map entered variable?

Answer 16

A map entered variable (MEV) represents values of a function in terms of its variable, this is useful in function with more than 4 inputs.

Question 17

How do we minimise a two-level SOP which includes MEV’s?

Answer 17

1. Ignore MEV’s and loop 1’s and X’s. Find the expression, F1
2. For each MEV loop only that MEV. E.g A’ looped separate to A and other letters. Find expression, F2,
3. Combine F1 and F2.