1999 Exam Solutions - Digital

# 1999 Exam Solutions - Digital - PART A Digital QUESTION 1...

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Unformatted text preview: PART A - Digital QUESTION 1 Suppose the decimal integer values ﬂour 0 to 255 are to be transmitted. (a) How many lines will be needed if parallel representation is used? (1)) How many lines will be needed if serial representation is used? A: (a) 8 (b) 1 QUESTION 2 (a) Convert the following numbers to decimal; (show all working) 1010101 1 1) 5A 11 1000010110001BCD (b) Convert the following numbers to binary; (show all working) A5 h 139 d 000110010101 BCD A: (a) 171, 90, Error BCD not possible (b) 10100101, 10001011,195 noooau QUESTION 3 One of DeMorgans’s Theorems is that Z + E = FB— Prove that the theorem also works for th‘reee variables. That is, prove Z+1§+ZF=ABC a.“ A:2+§+E= 3+5 LetDjAB .'.=,D+¥C‘ ‘ =55 =ABC Q.E.D. (2Marks) (2Marks) (3Marks) (3Marks) QUESTION 4 (a) Write the output expression for ﬁgure 1. ( 2 Marks) (b) simplify the output expression with boolean theorems. ( 3 Marks ) A:(a)ZE+ABC+AE+ABE=F (b)F=Z+E+ABC+Z+C+AB'C“ As C+E=I 3F=i F=0 QUESTION 5 A NC lathe employsa system for monitoring the lathes safety by monitoring sliding door, oil coolent and rotation status. These operate as follows: ” Door = 1 when sliding door is open. Oil = 1 when oil is present. Rotation Status = 1 when work piece is rotating Figure 2 shows the logic circuit that controls a warning light for certain combinations of safety conditions. Assume that a HIGH at output W activates the warning light. (a) Determine what conditions will give a warning to the operator. ( 3 Marks ) (b) Change the circuit to one using all NAND gates. ( 2 Marks ) QUESTION 6 An edge-triggered D ﬂip-ﬂop and a T ﬂip-ﬂop aren wired up as in ﬁgure 3. (a) Assume that Q = 0 initially, determine the Q waveform. ( 2 Marks ) (b) Describe the operation of this circuit. ( 3 Marks) 8KHz Figure 3 A: (a) Both devices set up to toggle so the ﬁnal Q output will be a square wave of 210-12 (b) This is a divide by 4 circuit QUESTION 7 Analyse the following circuit and draw its truth table. Is it ﬁmctionally the same as a NAND gate SR latch? ( 5 Marks) Yes, it is functionally equivalent ...
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