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1 Your Name: SI Number: UNIVERSITY OF CALIFORNIA AT BERKELEY BERKELEY AVIS IRVINE LOS ANGELES RIVERSIE SAN IEGO SAN FRANCISCO epartment of Electrical Engineering and Computer Sciences SANTA BARBARA SANTA CRUZ CS 5  Spring 998 Prof. A. R. Newton Prof. K. Pister uiz Solutions Room Evans Hall, :pm Tuesday April 7 th (Open Katz only, Calculators OK, hr mins) Include all final answers in locations indicated on these pages and in pen. Use space provided for all working. If necessary, attach additional sheets by staple at the end. BE SURE TO WRITE YOUR NAME ON EVERY SHEET.. (pts) (a) A digital system is required to amplify a binaryencoded audio signal. The user should be able to control the signal amplitude from minimum to maximum in increments. What is the minimum number of binary bits required to encode the userspecified amplitude? (b) Excess code (Katz page 499) is a variation of binarycoded decimal (BC) code. Each decimal digit is represented by a 4bit code that is three more than the associated BC code. For example, is encoded in excess as, is encoded in excess as, etc. esign a singleoutput combinational logic circuit that outputs a when the input to the circuit in 4bit excess code is a prime number. For all other (nonprime) legal 4bit excess numbers applied to the inputs, the output is a. Assume complement inputs are available and implement the circuit using: (i) One 6input, four controlline multiplexer only. (ii) One 8input, three controlline multiplexer only. (iii) One 4input, two controlline multiplexer and a minimum number of simple logic gates (INV, NAN, NOR, AN, OR, XOR, XNOR). (a) (5pts) Number of bits = _ 6 =64 and 7 =8 so seven bits are required () / () / () /4 TOTAL /. (b) (i) (5pts) One 6input MUX ecimal A B C Prime A B C (additional space for solutions on reverse) prime uiz Page of 6 CS 5  Sp. 98
2 . (b) (ii) (pts) One 8input MUX A B C prime. (b) (iii) (pts) One 4input MUX and logic gates C A B prime Additional space for Problem CS 5  Sp. 98 Page of 6 uiz
3 Your Name: () ( points) (a) What is the better way to implement arithmetic in a binary computer: one'scomplement or two'scomplement? Why? Include all of the arguments you can think of for and against your answer. (b) oes the statemachine opposite have any equivalent states? If so, which states are equivalent? Show all working. (c) esign a 4bit ripple upcounter using positive edgetriggered flip flops and a minimum number of combinational logic gates. Show the schematic diagram. / a / / c d / / b / / / (a) (pts) One's or two's complement? Why? 's complement + easier to do addition and subtraction (sum of ve #s) (can be done in one byteserial pass) + single representation for  must add for making ve #s (continue on reverse if necessary) (b) (pts) Equivalent states: a = b b c d a a c c X a b a c X a b a c X a b c (additional space for solutions on reverse) uiz Page of 6 CS 5  Sp. 98
4 .(c) (pts) 4bit ripple upcounter CLK Additional space for Problem CS 5  Sp. 98 Page 4 of 6 uiz
5 Your Name:. (4 pts) esign a Moore machine that detects the number 9 encoded in binary ( ) and in excess ( ). The machine should reset after each detection (i.e. overlapping sequences are ignored). Sample input (X) and output (Z) sequences are given below: X= Z= (a) raw a state transition diagram for the Moore machine. (b) Use an implication table to determine if any states are equivalent. If so, list the equivalent states and then redraw your (now minimized) state diagram. (c) Using flipflops and the stateassignment rules discussed in class, indicate all adjacency constraints for an optimal state encoding and determine an optimal encoding, listing the state codes for each state in the machine. (d) Write equations for the nextstate logic only (not the output logic) using a minimal NORNOR twolevel representation.. (a) (pts) State transition graph: Original After reduction (if changed) One answer (framed) S S S S 4 S S 5 S 6 No change. (b) (5pts) Implication table: normal table with no equivalent states (5pts) Equivalent States: None (additional space for solutions on reverse) uiz Page 5 of 6 CS 5  Sp. 98
6 . (c) (5pts) Adjacency constraints: Rule : {S, S, S 6 },{S, S 4, S 5 }, {S, S 6 } Rule {S, S },{S, S 4 }, {S, S },{S, S 6 }, {S, S 5 } Rule : {S, S, S, S, S 4, S 5 } (5 pts) Optimal state assignment (show Karnaugh map) B C A 4 S 6 S 5 S 5 7 B S S S S 4 6 C State codes: S =, S =, S =, S =, S 4 =, S 5 =, S 6 =. (d) (pts) Nextstate logic in NORNOR form (equations only!): A = ( B + C ) + ( C + X) + ( B + C ) + ( A + C ) = + X ) + ( + ) + ( + X ) + ( + + ) B ( A A B A A B C = ( + ) + ( + X ) + ( X ) C A B B C + Additional space for Problem CS 5  Sp. 98 Page 6 of 6 uiz
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