Cork Institute of Technology
Higher Certificate in Engineering in Electronic Engineering - Stage 1
(National Certificate in Engineering in Electronic Engineering – Stage 1)
(NFQ - Level 6)
Summer 2005
Digital Systems
(Time: 3 Hours)
Answer any five questions [20 marks each]
Maximum available marks is 100.
Examiners: Mr. J.J. O’Sullivan
Mr. J. Berry
Dr. R. O’Dúbhghaill
Q1 (a) Use a truth table to prove the Distributive Law of Boolean algebra below
A
(
B
+C)
=
A
B
+
A
C [4 marks]
(b) Using Boolean algebra only, minimise the following expressions
i)
X=ACB
+
BAC
+
C A B
ii)
Y=AB(A+C)+B(A+AB) [8 marks]
(c) Convert the following Boolean logic expression into standard sum-of-products
form.
Z=ABCD+ABCD
+
ABC
+
A BCD
+
ACD
+
ABCD [2 marks]
(d) Minimise the sum-of-products expression in (c) using a Karnaugh map. [6 marks]
Q2 In an automated bottling plant, a valve will open to fill each bottle when the bottle
moves into position, and the valve will close once the liquid in the bottle reaches the
full level. The plant is controlled by a logic circuit which has the following inputs
from sensors:- valve open (V), bottle in position (P), bottle full (F).
The output (Z) from the logic circuit will sound an alarm and stop the plant if the valve
opens before a bottle moves into position, or if the valve fails to close when a bottle is full.
For the logic circuit specified above,
(a) derive a complete truth table for the output (Z) [4 marks]
(b) from the truth table, obtain a sum-of-products expression [2 marks]
(c) using Boolean algebra or a K-map, minimise the expression [4 marks]
(d) for the minimised expression, draw a basic logic circuit [4 marks]
(e) convert this circuit to one using NAND gates only [6 marks]
