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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2010/
Module Title: Digital Systems 1
Module Code: ELTR
School: Electrical and Electronic Engineering
Programme Title: Bachelor of Engineering in Electronic Engineering
Programme Code: EELXE_7_Y1 EELES_8_Y
External Examiner(s): Dr A Donnellan
Mr I Kennedy
Internal Examiner(s): Mr J O’Sullivan
Instructions: Attempt any three questions. All questions carry equal marks. Ensure that you include the Return Sheet with your answer book.
Duration: Two hours
Sitting: Autumn 2011
Requirements for this examination: N/A
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
You are expected to present your material in a neat and clear fashion. Start each question on a new page. Remember that you have plenty of time for this exam – two hours for three questions.
Q1 (a) For each of the logic gates, OR, NAND and XNOR, write down the following: i) a logic symbol ii) a truth table iii) a Boolean expression [6 marks]
(b) Draw a logic circuit for the expression X B ( C A ) A B [5 marks]
(c) Using Boolean algebra only, minimise the following expressions: i) F CBA BAC ACB CAB ii) F AB ( B AC ) [7 marks]
(d) Draw a truth table for the function represented by the following symbol:
[2 marks]
Q2 (a) Why do we use hex numbers in digital systems? Construct a table showing the
decimal, binary and hex equivalents of all possible 4-bit binary numbers. [4 marks]
(b) Use the table in (a) to carry out the following conversions: i) B4E9 16 to binary ii) 1011011011 2 to hex [2 marks]
(c) Perform the following conversions showing all working i) 23 10 to binary ii) 110101 2 to decimal [4 marks]
(d) The two’s complement number system represents both positive and negative values. How can we identify negative values in this system? [1 mark]
(e) The number 11001010 2 represents an 8-bit two’s complement value. Convert this value to decimal – explain each step taken. [3 marks]
(f) Using 8-bit two’s complement numbers throughout, perform the following arithmetic operations in binary and indicate if the result is positive or negative in each case - show all working. i) 3710 – 2510 ii) 2510 – (^3710)
(Note: 25 10 = 11001 2 3710 = 100101 2 ) [6 marks]
Module Title: Digital Systems 1
RETURN SHEET
C
A
B
Y
Figure 2
+5V
0V
SN74LS08N SN74LS04N SN74LS32N
Figure 3
Name: Return this sheet with your answer book.
