# ECE 341 Midterm Exam

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1 ECE 341 Midterm Exam Time allowed: 90 minutes Total Points: 75 Points Scored: Name: Problem No. 1 (10 points) For each of the following statements, indicate whether the statement is TRUE or FALSE: (a) It is undesirable to use latches for building circuits that involve counters and shift registers. (b) Booth algorithm is most efficient when the multiplier has an alternating sequence of 1s and 0s. (c) An array multiplier typically requires less hardware than a sequential multiplier. (d) Subtracting a positive integer from a negative integer in 2 s complement binary arithmetic can cause an overflow. (e) A programmable device (such as an FPGA) usually achieves better performance than a customized device (such as ASIC) for a particular task. Problem No. 2 (12 points) (a) (6 points) The input waveforms for a positive edge-triggered JK flip flop are shown in the following figure. Assume that each waveform starts at time = 0 and output Q of the flip-flop has a logic value of 0 at time = 0. What is the logic value of output Q at the following points of time: (i) 18 ns, (ii) 35 ns, (iii) 50 ns?

2 (b) (6 points) Implement an XNOR function ( NOT gate. ) by using a 2-input multiplexer and a Problem No. 3 (18 points) You are required to design a 2-bit synchronous counter by using a finite state machine. The counter has one external input signal x, which dictate the operation of the counter as follows: (i) (ii) If x = 0, the counter counts up in the following sequence,0,1,2,3,0,1,2,3,0,1,2,.. If x = 1, the counter acts as a saturating down counter: It counts down until it reaches 0 and then stops there. The circuit also has an output signal z, which is equal to 1 only if the present value of the count is less than 3. (a) (6 points) Draw the state diagram for this state machine.

3 (b) (6 points) Assume that D-flip flops are used to store the two state variables y 2 and y 1 and the state variable assignment is done in such a way that the number y 2 y 1 represents the count value. Show the state-assigned state table. (c) (6 points) Derive the minimal logic expression to implement the output z and the next state value Y 2. You do not need to show the logic circuit implementation. Problem No. 4 (20 points) (a) (4 points) A 4-bit carry-lookahead adder (CLA) is used to add two numbers X(x 3 x 2 x 1 x 0 ) = 1101 and Y(Y 3 Y 2 Y 1 Y 0 ) = 1010 with an external carry-in c 0 = 1. Use the CLA carry-out equation to compute the value of carry-out c 3.

4 (b) (8 points) A multiplier circuit employing Booth algorithm is used to multiply two numbers +8 (multiplicand) and -5 (multiplier) expressed in 2 s complement binary notation. Show the Booth recording for the multiplier and calculate the product by using Booth algorithm. (c) (8 points) A company is designing a processor P1 to execute a program, whose instruction statistics are as follows: Type of Instruction Percentage of Total Instructions Cycles per Instruction Branch 10% 3 Load 30% 5 Store 20% 4 Arithmetic 40% 4 The chief architect for the processor sets a target that the processor must be able to execute 500 million instructions per second. What is the minimum clock speed that the processor must run at to achieve this target?

5 Problem No. 5 (15 points) The 5-stage RISC processor discussed in class is used to execute the following sequence of instructions, one after the other: Instruction 1: Load R4, 200(R3) Instruction 2: Add R5, R2, R4 Instruction 3: Store R5, 400(R3) The processor data path with all the control signals is shown in the following figure: Assume that the initial contents of registers R2, R3, R4 and R5 are 200, 28000, 800 and 70 respectively. The contents of memory locations at addresses 28000, and are 400, 500 and 600, respectively. (a) (9 points) For each of the three instructions in the program, answer the following questions: (i) Which of the two inputs ( 0 or 1 ) is selected by MuxB?

6 (ii) What are the contents of register RY after the completion of stage-4 ( memory access stage)? (iii) Write down the value of control signal RF_write during stage-5 of instruction processing. (b) (6 points) After the completion of the above code sequence, what are the final contents of memory locations at addresses and 28400?

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