CSCI 232 Exam #1

5 March 2003

Instructions: This exam is closed book, closed notes, closed neighbor, open mind. Write legibly since if I can’t read it, it is wrong. Read through the entire test first to find the easy problems and plan the most efficient use of your time. There are 100 points on this test, not counting the bonus. Good luck, and have fun!

I. Data Representation (35 points)

a. (5 points) Convert the binary number 1101001010010101 into hexadecimal.

b. (5 points) Convert the octal number 10100011 into hexadecimal.

c. (5 points) Convert the number 142 to a binary representation of the BCD equivalent.

d. (5 points) What is the two’s complement representation of the number -16 using 8 bit integers?

e. (5 points) Subtract 11 from 5 using 4 bit 1’s complement arithmetic.

f. (5 points) Describe a technique for detecting all one bit errors in a computer word.

g. (5 points) What property of character codes is necessary in order for sort programs to work correctly?

II. Combinational Logic (20 points)

a. (10 points) Simplify the expression AB + ACD + ACD’ using Boolean algebra.

b. (10 points) Simplify the expression A’B’CD + A’BCD + AB’CD + ABC’D + ABCD’ + ABCD using a Karnaugh map.

III. Sequential Logic (10 points)

a. (10 points) Show how to use JK flip-flops and some combinational logic to implement a D flip-flop.

IV. Digital Components (20 points)

a. (10 points) Show how to implement a 3x8 decoder using two 2x4 decoders.

b. (10 points) Build a 4 bit shift register using D flip-flops.

V. RTL and Micro-ops (15 points)

a. (5 points) Describe two methods of implementing a data bus that prevent the outputs of multiple registers from colliding.

b. (10 points) Show how to use 4 full adders to build a circuit that can either add or subtract two 4-bit numbers.

VI. Bonus (5 points) A date is said to be odd if all the digits that make up that date are odd. Similarly, if all the digits are even, then the date is said to be even. Recently we had the last odd date to occur for some time. What was that date, and when will the next odd date be? (As an example, 3/4/2003 is neither an even or an odd date since 3 is odd, but 0, 2, and 4 are even.)

Bonus (5 points) For each of the following chips describe what it contains (include the number of functional units per chip):

Example: 7402 … quad 2-input NOR gate

a. 7400

b. 7432

c. 7476

d. 7483

e. 74153