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Unformatted text preview: ECE 2030
Section C Exam ll Solutions
October 10th, 2008 1. Consider the Boolean function deﬁned by the following truth table. a. Using K—Maps provide a simpliﬁed POS form of the Boolean expression for this truth table. Show the KMap and explicitly list all prime implicants, and mark those which are essential. b. Illustrate the hnplementation of your SOP solution on the PLA shown below 2. Fill in the truth table for the following circuit. Each block is a 41 multiplexer. For clarity, the select
lines, S 1, and SO are not shown in the ﬁgure, but are connected to all blocks in the same way. 3. Show the block diagram implementation of a 116 de—multiplexor using 14 de—multiplexors. Show the
truth table for the design. Be sure to document the notation you use. 4. You have four devices, A, B, C, and D, connected to the controller box below, each with a unique 4bit
ID as shown. Each device will place a 0 or 1 on its input and the device priority from highest to lowest
is B9D9A9C. The controller should output the device ID of the highest priority requesting device. Show a feasible design for the controller using a priority encoder and a ROM. You must i) provide the
truth table for the priority encoder, ii) show the contents of the ROM, and iii) show all of the signals
connecting the two blocks and the controller inputs and outputs. You do not have to provide a gate
level design of the priority encoder. ' Device m A
A (4)16 B
B (5)15 C (6)16 C
D (7)26 D ID3 lD2 IDl lDO WW '1 Ebb 6 5. Convert the following numbers from one notation to the other. a. Fill in the following table. The ﬁxed point format is a 12 bit number with a 4 bit fractional
component. The ﬂoating point number uses the IEEE 754 format. Binary Fixed Point Sin le Precision Floating Point (in Hex)
12.5625 loo.loc>l 0x y 0900
um ' m o xooo 800w may) b. What is the magnitude of the error (relative to the truncate rounding mode), if any, when the
following computation is performed assuming the availability of 4 signiﬁcant bits. 1.01x2122+1.1x2128 IcQ—S'
oo oooom DI 9K 651 6. Number systems
21. Provide the ASCII encoding of “Test” in a 32bit word I‘M; 73 7‘! b. Identify which of the following numbers would satisfy a lessthan test. If 0x80000004 Dr 0x12345678 (IEEE 754 Floating Point)
2. OXTOOOOOOOa 0x800001 (2’s complement) 807% we Macy/5k
Q”); 661» 7. Perform each of the following arithmetic operations for three different interpretations of the number representation — 1’s complement, 2’con1p1ernent, and unsigned. All representations use 6 bits. For each
case, indicate if overﬂow has occurred. 110110 Overﬂow? 101100 Overﬂow?
+ 111000 +101100 mm Yes@ m@m
Yes/6) 0 (wow) O l O 1 2 3 4 ASCII Table 5 6 7 8 9 A B C NUL SOH STX ETX EOT ENQ ACK BEL BS HT LF VT FF DLE DCl
SP '
O l
@ A
P Q
‘ a
P q DC2 DC3 DC4 # 3 $ NAK SYN ETB CAN EM
% & ‘ i ) 5 6 7 8 9 SUB ESC FS
* + I , <
J K_ L
Z [ \
j k l
2 { i CR GS E F
so SI
RS US
/ > 'P N 0 1‘1 0 ~ DEL 10 ...
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 Spring '10
 Wills

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