Last Name: _______________ First Name __________________CS 150 - Sp. 92 Page 1 of 6 Quiz2UNIVERSITY OF CALIFORNIA AT BERKELEYBERKELEY • DAVIS • IRVINE • LOS ANGELES • RIVERSIDE • SAN DIEGO • SAN FRANCISCO SANTA BARBARA • SANTA CRUZDe p a rtm en t of Ele ctrica l En gin e e rin g and Com p u ter Scien c esCS 1 5 0 - Sprin g 1 99 2 Pro f. A. R. Ne wto nQuiz 2Room 10 Evans, Tuesday 3/31(Open Katz, Calculators OK, 1hr 20min)Include all final answers in locations indicated on these pages. Use reverse side of sheets for all working. If necessary,attach additional sheets by staple at the end. BE SURE TO WRITE YOUR NAME ON EVERY SHEET.(1) (a) The binary string “10110101” is the 8-bit two’s complement representation of a fixed pointnumber. What is its decimal value?1(a) (5pts) 10110101 = _______10(b) Design a circuit to compute the two’s complement of a 3-bit binary number. The inputs are b0,b1 and b2, where b2 is the most significant digit and the outputs are c0, c1 and c2 where c2 is themost significant digit.(i) Show a truth table for the circuit.(ii) Draw Karnaugh maps for each output and use them to simplify the functions.(iii) Draw a schematic diagram using the minimum number of NAND gates and invertersonly.1(b) (15pts)(i) Truth table:1(b) (ii) Karnaugh Maps:Last Name: _______________ First Name __________________CS 150 - Sp. 92 Page 2 of 6 Quiz2 00 01 11100105731462 00 01 11100105731462 00 01 11100105731462(iii) Schematic diagram:Last Name: _______________ First Name __________________CS 150 - Sp. 92 Page 3 of 6 Quiz2(2) You are to design a “Manhattan Compass” which is an automobile accessory which has four displaylights labelled North, South, East, and (yes, you guessed it...) West. One of the lights is always litand indicates which direction the car is facing. There are two sensors on the steering wheel, labelledRight and Left. The wires connected to each of the right and left sensors has the value 1 when theposition of the steering wheel is to the right or left of center respectively and a value of 0 otherwise.In addition, there is a button labelled INIT which, when pushed, tells the system that the car isstationary, the steering wheel is centered (neither right nor left) and the car is facing north. InManhattan, all turns are exactly 90 degrees once initiated (U turns are not permitted). Your designis to be a clocked synchronous circuit of the Moore form. Assume the clock signal CLK isderived from the left and right signals.(a) Provide a state transition graph for a Moore implementation of the compass. Use the minimumnumber of states.(b) Provide a state table for the compass.(c) Derive the flip-flop input equations and compass output equations for an implementation whichuses clocked D flip-flops. Assume the INIT signal is used to reset the flip flops. Draw a schematicdiagram for your circuit, including the D flip-flops and a minimum number of logic gates (nomultiplexors!). Show all Karnaugh maps used.2(a) (4pts) State Transition Graph:2(b) (2pts) State Table:Last Name: _______________ First Name __________________CS 150 - Sp. 92 Page 4 of 6 Quiz22(c) (i) (2pts) Karnaugh Maps:(ii) (6pts) Flip-flop Input Equations & clock generation:__________________________________________________________________________________________CLK = _____________(iii) (4pts) Output Equations:N = ________________ E = _________________S = ________________ W = ________________(iv) (7pts) Schematic Diagram:Last Name: _______________ First Name __________________CS 150 - Sp. 92 Page 5 of 6 Quiz2(3) Consider the state table for a Mealy machine shown below:next state output Zx=0 x=1 x=0 x=1S0S1S20 0S1S3S20 0S2S1S40 0S3S5S20 0S4S1S60 0S5S5S21 0S6S1S60 1(a) Draw a state transition graph for the machine showing all input/output transitions and symbolicstates.(b) Use the guidelines presented in class for state assignment to select an optimal state assignment (forminimum logic). Show all constraints, your final state assignment, and indicate whichconstraints are not satisfied by the assignment.(c) If a ROM where used to implement the next-state and output logic for a D-flip-flop-basedimplementation of your machine, how big would it have to be?3(a) (4 pts) State Transition Graph:Last Name: _______________ First Name __________________CS 150 - Sp. 92 Page 6 of 6 Quiz23(b) (i) (6 pts) Constraints:Guideline 1: _________________________________Guideline 2: _________________________________Guideline 3: _________________________________( ii) (3 pts) Karnaugh Map for Assignment: 00 01 11100105731462(iii) (3 pts) Final State Assignment:S0 = _____ S1 = _____ S2 = _____S3 = _____ S4 = _____ S5 = _____ S6 = _____(iv) (3 pts) Constraints not satisfied:________________________________________________________________________________________________________3(c) (6pts) ROM size:Number of address lines: ______Number of data bits at each address: ________Total number of ROM bits:
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