Ics151 Fq05 Final

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ICS 151 Digital Logic Design, Fall Quarter2005, Final Page 1

ICS 151Final

Name : _________________ , _________________(Last Name) (First Name)

Student ID : _______________

Signature : ________________

Instructions:

1. Please verify that your paper contains 15 pages including this cover.

2. Write down your Student-Id on the top of each page of this quiz.

3. This exam is closed book . No notes or other materials are permitted.

4. Total credits of this final are 80 points + 10 EXTRA CREDIT. 5. To receive credit you must show your work clearly.

6. No re-grades will be entertained if you use a pencil.

7. Calculators are NOT allowed.

Q1 Q2 Q3 Q4 Q5 Q6[ExtraCredit]

Total Credit 15 10 15 10 30 10

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Question 1. [Multiple choice] Select the correct answer:

[NO CREDIT UNLSESS YOU SHOW YOUR COMPLETE WORK]

a. What is -75 in 2s complement? [3 points]

2. (B5) 16

75 = 01001011-75 = 10110100 + 1 = 10110101 = B5

b. How many 4-to-1 multiplexers should be used to make a 64-to-1 multiplexer?what is the critical-path-delay of a 64-to-1 multiplexer in terms of the number oftwo-input gates?

[3 points]

3. 21, 12

16+4+1 = 21 MUXEach MUX has:1 level of 3 input AND + 1 level of 4 input OR => 4 levels of 2-input gate

3 levels of MUX * 4 levels of 2-input gates = 12

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c.

What is the result of Boolean expression simplification for :BC + D (A + B) + BCD + ABC

[5 points]3. B + D

Use K-MAP

d. How many 2k*4-bit RAM modules do we need to compose a 64k*12 RAMmodule? What should be the size of decoder?

2. 96, 5-to-32[4 points]

(64/2) * (12/4) = 96 ram modules32 rows of ram modules => 5-to-32 decoder

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Question 2 [Mealy machine design] [10 points]

Draw the FSM diagram for a Mealy machine that can detect the pattern 1011 on a streamof binary values arriving as input x and generating output z=1 when the pattern isdetected. Your model should also be able to detect overlapping sequences.

Input/Output

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Question 3 [Sequential circuit analysis] [15 points]

Analyze the circuit given below ( x is input and z is output):

a. Write the equation for flip-flops inputs (D1, D0) and the circuit output (z) [3points]

D1 = S1S0X + XS0D0 = X(S1 + S0)Z = S1S0

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b. Fill the state table based on the input equation for flip-flops: [6 points]

Present state Input Next state OutputS100001111

S000110011

X01010101

D1(n1)00100110

D0(n0)01010100

Z00000011

c. Draw the FSM of the circuit based on the state table driven in part (b) [5 points]

d. Guess the functionality of the circuit. [1 points]101 Detector

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Question 4 [C to RTL transformation] [10 points]

Here is a C program that computes the square root of an integer number x:

temp = 0;While (temp * temp < x)

temp++;sqrtx = temp;

Convert this C program to an FSMD (high-level behavioral state machine)(Note: Just draw the FSMD, no need for any other step)

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Question 5 [RTL-based design] [30 points]

We want to design a circuit that finds an 8-bit input value X inside a 1024*8 memoryand return the index of the value when it is found in memory otherwise it returns -1. Thecircuit begins when a START signal is set to 1 and asserts a DONE signal atcompletion.

a. Capture a high-level state machine [10 points]

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b. Create the datapath using the components (as many as needed) listed below:

a. RAMb. Adderc. Comparatord. Register

[10 points]

Two notes:1. cnt_reg is a 10-bit register. Ret_reg is an 11-bit register. Adder is a 10-bit adder.2. You can remove MUX, by using a register that has PRESET input and activatethe PRESET in initialization cycle that makes ret_reg=111 1111 1111

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c. Connect the datapath to controller [5 points]

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d.

Derive the controllers FSM diagram [5 points]

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Question 6 [Pipeline utilization] [10 points: EXTRA CREDIT]

a . Using Adder, Subtractor, and Multiplier, design a circuit that performs the followingoperation: [1 point]

Z = (A+B)*(C+D) (E+F)*(H+G)

A, B, C, D, E, F, G, H and Z are 8 bit registers.

b . If addition/subtraction takes 10 ns and multiplication takes 25 ns, what is the fastestclock frequency for the above circuit? [1 points]

freq = 1/45ns = 22.2 MHz

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c. Add pipeline registers to your design in part (a) to make your design as fast aspossible. [2 points]

d . What is the fastest clock frequency for the pipelined version in part (c)? What islatency for this circuit? [2 points]

freq = 1/25 = 40 MHzlatency = 3 * 25 = 75 nS

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e. Consider the schedule below for computing Z = (A+B)*(C+D) (E+F)*(H+G) that

uses 5 adder/subtractors and 2 multipliers:

Draw a new schedule that uses only 2 adders/subtractor and 1 multiplier. How manycycles it will take to compute a new value for Z? [2 points]

4 cycles

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f.

Draw the new datapath based on the schedule in part (e) [Hint: Add the requiredmultiplexers] [2 points]

Ics151 Fq05 Final

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