Name: SS#:

CAD of Digital VLSI

Ralph Etienne-Cummings

Exam 1: Digital Systems Fundamental, Integrated Electronics and Computer Systems Fundamental (1.5 hours, Open book)

September 18, 2001

Attempt all questions. Show all calculations to obtain partial credits. If you run out of time, outline how you would approach the problem.

P1: (25 pts) You are to design an adder that operates on two, 2-bits numbers.

(a)Construct the truth table for the adder. (5 pts)

(b)Obtained the simplified expressions for the adder. (5 pts)

(c)Draw the schematics of the expressions. (5 pts)

(d)Convert the expressions to NAND only implementation. (5 pts)

(e)Convert the expression to NOR only implementation. (5 pts)

P2: (25 pts) Provide an intuitive proof that the above-threshold drain-current of a MOSFET:

Where Cgate is gate capacitance per unit area, W is the width of the transistor, L is the length of the transistor and Vgate is the gate voltage.

P3. (25 pts) Consider the circuit in figure P3. Assume Kn =20uA/V2, Kp=10uA/V2, Vton = |Vtop| = 1V, =0 and =0 V-1.

(a)There is a significant mistake in the circuit that will make it unoperational un normal circumstances. Can you identify the mistake? How would you correct it? (5 pts)

(b)Compute Vo if Vin = 0V and 5V. (5 pts)

(c)Sketch the transfer function as Vin is swept from 0V to 5V. (10 pts)

(d)Draw the cross-section of the circuit, showing all relevant connections, parasitic diodes and capacitors and shapes of the channels when Vin = 5V. (5 pts)

P.3

P4. (25 pts)

(a)2’s complement binary number representation is often used to perform arithmetic in a CPU. Explain what 2’s complement numbers are and why they are used. (5 pts)

(b)Using 2’s complement representation, compute 21 – 17. Show all calculations in binary format and state all assumptions made. (5 pts)

(c)If a computer is design with a 16b instruction format. Assuming that the opcode portion of the instruction is 4b wide, what is the largest memory that can be addressed using a single instruction? (5 pts)

(d)What are the three basic phases of a CPU’s instruction cycle? (5 pts)

(e)You purchase a new computer that doubles the CPU clock speed of your current machine. The clock speed doubling is the ONLY difference between the two machines. You compile and run a large program and you notice that the speed-up under identical run conditions is not doubled. Provide some explanations for your observations? (5 pts)

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