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ENEE244 (sec 201-206) Spring 2006
Final Examination Pages: 9 printed sides
Name: ______ ____________ ________________________ Time alloted: 2 hours Student ID: ______________________________________ Maximum score: 100 points
University rules dictate strict penalties for any form of academic dishonesty. Looking sideways will be penalized. Look at only your own exam at all times.
There are 14 questions, some with subparts. Read them carefully to avoid throwing away points!! Write your answer in the space provided. Closed book, closed notes, no calculators.
Partial credit rule: Must show your intermediate steps clearly for partial credit!
1. Convert (23.875) 10 into a binary number. (6 points) 2. Convert (735) 8 to a hexadecimal number. Do not convert to base 10 as an intermediate step. (4 points)
3. A computer stores signed integers in 6-bit two’s complement form. If X = 18 and Y = -23, then show how this computer performs X + Y. (Show your steps and the answer as stored in computer). Is there an overflow? (8 points) 4. What is one advantage of the 2421 BCD code over the 8421 BCD code? (1-2 sentences). (3 points)
7. Is the NOR operator associative? Show why or why not. (6 points) 8. Does some function F=x(y+z') imply function G=xy + yz' + xz? Show why or why not without drawing the K-map. (6 points)
9. A Boolean function takes a BCD digit abcd as input, and outputs a single bit f which is 1 when the digit is one of 3,4,5,7,8, or 9; otherwise f is 0. Unused 4-bit combinations in BCD digits are don’t care inputs. (8 + 4 = 12 points) (a) Minimize f using a K-map into a sum-of-products minimum expression.
(b) Minimize f using a K-map into a product-of-sums minimum expression.
11. In a commercial device we are designing, we want to simultaneously compute two functions F and G of the same three 1-bit inputs x,y, and z. F=1 whenever the number xyz is greater than 2, and 0 otherwise. G=1 when any two of x,y and z are equal but different from the third. (4 + 6 =10 points) (a) Draw the truth tables for F and G.
(b) We have a choice of encoders, decoders, multiplexors and demultiplexors to implement F and G. However our cost budget allows the use of only ONE INSTANCE OF ONE TYPE of any of these components for each device, along with at most two multi-input gates if necessary. Which one component will we choose? Draw a circuit to simultaneously compute F and G using that one component instance.
12. A T flip-flop is loaded with an initial value of 0. Thereafter in N successive cycles the N bits of a number X=xn ... x1 are provided on the T-input of the flip-flop, from least significant to most significant. What function of X does the flip-flop contain after N cycles? Do not use a formal analysis procedure; instead use your intuition. Your answer can be stated in English instead of a formal Boolean expression. (5 points)
13. Consider a Moore machine circuit that takes two bits x and y as input and has a single bit output z. It outputs z=1 if there has been any successive 5 bits appearing in x and y simultaneously that are equal, at any time in the past. An example desired input/output sequence is:
x = 00101001010010101110 y = 01101111010001101111 z = 00000000000011111111 (6 + 4 = 10 points) (a) Draw a state diagram for this circuit. State what initial value, if any, should be loaded into the flip-flops for correct operation.
(b) Suppose the circuit above is designed by someone else. (Please do not design it yourself!). We wish to modify their design to remove the requirement for the circuit to be initialized. Show a simple way to modify the design that adds an extra start input S, such that when S=1, the circuit behaves as if it were in the start state. Otherwise, when S=0 the circuit behaves as normal. Assume that the start state is encoded as all zeros. ( Hint : Describe how each bit of the flip-flip inputs or outputs should be modified, without changing anything else in the circuit)
