April 2000
LD201 : LOGIC DESIGN

QUESTION 3

Total Marks: 15 Marks

• Question 1
• Question 2
• Question 4
• Question 5
• Cover Page

Click to access
SUGGESTED SOLUTIONS
for Question 3

A beer-bottling factory contains a production line for putting caps on bottles. The production line consists of a bottle-capper and three bottle fillers, you have to design a warning system to indicate whether the bottle-capper is being overloaded by the bottle-fillers.

The bottle-capper C has two different operation states: normal, in which it can handle 60 bottles per minute, and super, in which it can handle 75 bottles per minute. The bottle-capper is fed from three bottle-fillers F₁, F₂, F₃, which fill 50,30 and 20 bottles per minute respectively. The factory operates on a 24-hour basis, so at any one time at least one bottle-filler is in operation. The warning device W should light up when the output of the bottle-fillers exceeds the capacity of the bottle-capper.

(a) Draw a truth table describing the behavior of W in terms of C, F₁, F₂, F₃. For C, use ‘1’ to mean the bottle-capper is running in super mode, ‘0’ for normal mode. [3 marks]

(b) Give an unsimplified sum-of-products expression for when W should light up. [2 marks]

(c) Draw a Karnaugh map for this expression, and hence derive simplified sum-of-products and product-of-sum forms of the expression. [4 marks]

(d) Using the laws of boolean algebra, show that these two expressions are logically equivalent. Identify the laws used. [3 marks]

(e) Draw a circuit showing an implemention of the simplified sum-of-product expression, using AND, OR and NOT gates. [3 marks]