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4 problems, 5 pages Exam Two Solution 27 October 2010
Problem 1 (3 parts, 21 points) State Part A (8 points) Implement a transparent latch using only inverters and pass gates. Label the inputs In and En , and output Out.
Part B (7 points) Consider a register with a selectable write enable (WE) and read enable (RE). It is implemented with transparent latches, a 2 to 1 mux, and a pass gate. Describe its behavior by completing the output values. Also indicate when a write and/or a read is being performed.
Register
IN OUT WE RE φ 1 φ 2
IN WE RE CLK OUT write? read?
A 0 0 ↑↓ Zo
A 1 0 ↑↓ Zo ✔
A 0 1 ↑↓ Qo ✔
A 1 1 ↑↓ A ✔ ✔
Part C (6 points) Assume the following signals are applied to a register with write enable Draw the output signal Out. Draw a vertical line where In is sampled. Draw crosshatch where Out is unknown.
Φ^1
Φ^2
WE
In
Out
4 problems, 5 pages Exam Two Solution 27 October 2010
Problem 2 (4 parts, 40 points) Number Representations & Arithmetic Part A (10 points) Convert the following notations: decimal notation binary notation 327 101000111 37.5625 100101. 44.125 101100. octal notation hexadecimal notation 73.37 111011.0110111 = 3B.7C 1011010.1101 = 132.64 0x5A.D Part B (12 points) For these 12 bit representations, 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. All signed representations are two’s complement. representation most positive value step size unsigned integer (12 bits). (0 bits) 4K^1 signed fixed-point (6 bits). (6 bits) 31 63/64^ 1/ unsigned fixed-point (8 bits). (4 bits) 255 15/16^ 1/ signed fixed-point (10 bits). (2 bits) 511 3/4^ 1/ Part C (6 points) A 29 bit floating point representation has a 17 bit mantissa field, a 11 bit exponent field, and one sign bit.
What is the largest value that can be represented (closest to infinity)? 2^1023
What is the smallest value that can be represented (closest to zero)? 2 -^1024
How many decimal significant figures are supported? 5
Part D (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 fixed-point and six bit two’s complement fixed-point representations.
result 1. 11 1000.11 100.11 1.
unsigned error? □ no ■ yes ■ no □ yes □ no ■ yes ■ no □ yes signed error? ■ no □ yes □ no ■ yes ■ no □ yes ■ no □ yes
4 problems, 5 pages Exam Two Solution 27 October 2010 Problem 4 (3 parts, 24 points) Counters Part A (7 points) Implement a toggle cell using only transparent latches and basic gates (XOR, AND, OR, NAND, NOR, NOT). Use an icon for the transparent latches. Label the inputs TE , CLR , Φ 1 , Φ 2 and the output Out.
In Out En Latch
In Out En Latch TE Out CLR Φ (^1) Φ 2
Part B (8 points) Now combine these toggle cells to build a divide by 24 counter. Your counter should have an external clear, external count enable, and five count outputs O 4 , O 3 , O 2 , O 1 , O 0. Use any basic gates (AND, OR, NAND, NOR, & NOT) you require. Assume clock inputs to the toggle cells are already connected. Your design should support multi-digit systems.
O^0
O 1
O 2
Ext Clr
Ext CE
TEOut Clr
TEOut Clr
TEOut Clr O^3
TEOut Clr
TEOut Clr
O 4
4 problems, 5 pages Exam Two Solution 27 October 2010 Part C (9 points) Build a military timer (HH:MM) which displays hours (0...23) on the left and minutes (0...59) on the right as follows. In the diagram below: a) Fill in the label “Divide by ” on each counter.
b) Label the number of output wires coming from each counter to its attached display. c) Draw the appropriate wiring connections to allow this military timer to correctly respond to external clear (Ext CLR) and count enable (Ext CE) signals, and to correctly increment the hour count when the maximum number of minutes have passed while the clock is still running. Use any basic gates you require. Assume clock inputs are already connected.
Ext CLR Ext CE
CLR CE
Out
Max Count
Divide by 60
CLR CE
Out
Max Count
Divide by 24
(a) (a)
(^5) (b) (^6) (b)
