# ECE 2030B 1:00pm Computer Engineering Spring problems, 5 pages Exam Two 10 March 2010

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1 Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate the pages of the exam. For maximum credit, show your work. Good Luck! Your Name (please print) total

2 Problem 1 (3 parts, 22 points) Building Blocks Part A (6 points) Implement a 1 to 2 demultiplexor with pass gates and inverters. Be sure to label all inputs and outputs. Part B (8 points) Suppose the circuit below has the following input priority: I 2 > I 3 > I 0 > I 1. Complete the truth table by filling in the input values that would produce the given outputs and derive a simplified expression for O 1. I 3 I 2 I 1 I 0 V O 1 O 0 I0 I1 I2 I3 O0 O1 0 X X O 1 = Part C (8 points) Which building block does the following circuit implement? Label all inputs and outputs by filling in the squares. This implements a. In0 In1 En 2 to 4 decoder

3 Problem 2 (3 parts, 28 points) Number Systems Part A (10 points) Convert the following notations: binary notation hexadecimal notation decimal notation octal notation F3.DC Part B (12 points) For the 32 bit representations below, determine the most positive value and the step size (difference between sequential values). All answers should be expressed in decimal notation. Fractions (e.g., 3/16ths) may be used. Signed representations are two s complement. representation most positive value step size unsigned integer (32 bits). (0 bits) (24 bits). (8 bits) (28 bits). (4 bits) (16 bits). (16 bits) Part C (6 points) A 24 bit floating point representation has a 15 bit mantissa field, a 8 bit exponent field, and one sign bit. What is the largest value that can be represented (closest to infinity)? What is the smallest value that can be represented (closest to zero)? How many decimal significant figures are supported? 2 2 3

4 Problem 3 (3 parts, 24 points) Adding & Subtracting Part A (12 points) For each problem below, compute the operations using the rules of arithmetic, and indicate whether an overflow occurs assuming all numbers are expressed using a six bit unsigned and six bit two s complement representations. result unsigned error? signed error? Part B (4 points) Complete the truth table below for a full adder A B C in C out Sum Part C (8 points) Implement the full adder using only NAND, XOR, and inverter gates. Label inputs A, B, and C in. Label outputs C out and Sum. 4

5 Problem 4 (4 parts, 26 points) Registers and Latches Part A (6 points) Implement a transparent latch using gates of any type (e.g., AND, inverter, pass gates), but use the minimum number of transistors. Label the inputs In and En, and output. Part B (7 points) Design an RS latch using NOR gates only. Label inputs R and S. Label outputs OUT and OUT. Do not attempt to employ mixed logic notation. Also complete the truth table. R S Part C (5 points) Expand the RS latch to an implementation of a two-phase non-overlapping clock, generated from an input signal In that is a periodic square wave. Use only an RS latch and basic gates (AND, OR, NAND, NOR, and inverters). Label the input In and the outputs F1 and F2. R S OUT OUT Part D (8 points) Assume the following signals are applied to a register with write enable. Draw the output signal. Draw a vertical line where In is sampled. Assume is initially zero. Φ 1 Φ 2 WE In 5

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