Download Exam Solutions for ECE 2030B Computer Engineering Fall 2009 - Problem 1 to 4 and more Exams Computer Science in PDF only on Docsity!
4 problems, 5 pages Exam Two Solutions 4 March 2009
Problem 1 (4 parts, 24 points) Building Blocks Part A (8 points) Consider the circuit below. Complete the truth table. Then state what logical function this circuit implements.
A B Out
I 0
I 1
I 2
I 3
O
O 3 S 1 S 0
O 2
O 1
O 0
I 1
I 0
En (^) oops!
A B Out 0 0 1 1 0 0 0 1 0 1 1 1 This wacky circuit is Even Parity (XNOR) Part B (6 points) Consider the following circuit below. Determine its input priority.
I 3
I 2
I 1
I 0
O 1
O 0
I 0 I 1 I 2 I 3 V O 1 O 0
0 0 0 0 0 X X
1 0 0 X 1 0 0
X 1 0 X 1 0 1
X X 1 X 1 1 0
I 2 > I 1 > I 0 > I 3
Part C (4 points) Derive a simplified expression for O 1. O 1 = I^ 2 ๎ I^ 0 โ
I^ 1 Part D (6 points) Implement a 2-input NAND using a 2-to-4 decoder and a single OR gate (which may have any number of inputs). Label the inputs A and B , and output A NAND B.
IN 0
O 0 decoder^ 2 to 4 IN 1
O 1 O 2 O 3
A B
A NAND B
4 problems, 5 pages Exam Two Solutions 4 March 2009 Problem 2 (3 parts, 28 points) Number Systems Part A (10 points) Convert the following notations: binary notation decimal notation 110 0 1010. 128+64+8+2 = 202 1010 0100.1000 1 128+32+4+0.5+0.03125 = 164. 111 1100.11 64+32+16+8+4+0.5+0.25 = 124. octal notation hexadecimal notation 4 733.6 1001 1101 1011.1100 = 0x9DB.C 24 .32 01 0100.0110 1000 = 0x14. Part B (12 points) For the 16 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 twoโs complement. representation most positive value step size unsigned integer (16 bits). (0 bits) 64K-1^1 signed fixed-point (11 bits). (5 bits) 1023 31/32^ 1/ signed fixed-point (9 bits). (7 bits) 255 127/128^ 1/ signed fixed-point (14 bits). (2 bits) 8K-1/4^ 1/ Part C (6 points) A 34 bit floating point representation has a 24 bit mantissa field, a 9 bit exponent field, and one sign bit.
What is the largest value that can be represented (closest to infinity)? 2^255
What is the smallest value that can be represented (closest to zero)? 2 -
How many decimal significant figures are supported? ___ 7 _____
4 problems, 5 pages Exam Two Solutions 4 March 2009 Problem 4 (3 parts, 24 points) Registers and Latches Part A (8 points) Implement a transparent latch using only inverters and pass gates. Label the inputs In and En , and output Out.
EN
In Out
Part B (10 points) Implement a register below using needed muxes, latches, pass gates, and inverters (all in icon form). Complete the behavior table at right. Recall that the CLK signal indicates a full ฮฆ 1 ฮฆ 2 cycle; so the output should be the value at the end of a cycle (with the given inputs).
In Out
In Out LatchEn In Out LatchEn
WE RE
In0Out In1S
Part C (6 points) Assume the following signals are applied to your register. Draw the output signal Out. Draw a vertical line where In is sampled. Assume Out is initially zero.
WE
In
Out
In WE RE Clk Out
A 0 0 โโ Z 0
A 1 0 โโ Z 0
A 0 1 โโ Q 0
A 1 1 โโ A
