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Unformatted text preview: CS MélA/EE Mlﬁ FINAL EXAM
* Closed books and notes ~
(8 problema 180 minutes)
PLEASE BE SYSTEMATIC, ORGANIZED, and NEAT:
* this will be considered in the grading. December 137 2002. Mwa Name; Problem Points Score 1 20
2 10
.3 11
" 44 125*
5 8
6 13
7 13
8 10 Total 1 100 Problem 1. ('20 points) Design a sequential system which recognizes the pattern 0101011. a) [6 points] Complete the following state diagram. Each state is labeled with a sequence
that it ”rec0gnizes”. The correspondence between the state assignment an d sequence that it detects is shown
in the next table. State Sequence
5 start ‘
5’1 0
1 5'2 01
S3 010
S4 0101
S 01010
010101 b) [4 points] Encode these states using three state variables (y2,y1,yg) so that the state
assignment of state Si is the radix? representation of 0'. Complete tle state and transition
table: PS Input Input y2y1yo $=0§$21$=0 03:1
50 000 009.0 I 000,0 000, 000
51 «‘26?! man 0:349 ’00:: op,
52 {Sim 015:9 (mam 05>! 0m
53 DH Muss mats are Wm
34 1am? IOMQ @ﬂém Dal 1:220
55 {at ca Me 133? It? 10 Ca 0H 5'6 smygggemt “‘5‘! l1 f; 10
Y2 Y1 Yb, 2 T213110 c) [6 points] Implement the network using NAND gates and T ﬂip—ﬂops. Indicate the T
inputs in the state table. Give minimal sum of products expressions for T inputs. Show
the logic diagram of the network. d) [4 points] If the propagation delays are tp : 3.5ns, tsu = 0.9713, tNAND = 2723,
tn 2 1.5713, and tom; 2 2.5725, determine the maximum clock frequency. 'Tkwﬂgm 3: M4 a; Egg, M + “E;:::( Wréfﬂ/
a; G3 a 23/
(3% F (, aw?) 1 %.“ a, m :2 2 k 2 + a a} m. A .q M
yéq‘iﬂ m 31 + my? “3* QM Er? M) aaswmm g; m, :;,_ Wk“ Mfﬂ is
C m j H914 Problem 2. (:10 points) Derive the state transition/output table for the implementation of the
sequential system shown in the ﬁgure below. The next State and output functions are
implemented by a PLA structure. The machine has one input I and one output Z. Show
expressions for the ﬂip—ﬂop inputs. Show the state transition/output table. CLK @ﬁﬁc—«N Problem 3. (14 points) [8 points] Design a cyclic counter with the output sequence 0,1,4,7,6,3,0,1, . .. (of
period 6) using JK ﬂip—ﬂops and AND, OR7 NOT gates as needed. Assume that the input
a: is aiways 1. Seiect a. state assignment that is the same as the coding for the output,
that is 2U) : 5(13). Show the state/output table. Minimize all expressions. Show the
logic diagram of the counter. State / output table: Mg I} mi '
We) WE «w «I (b) [6 poin 1,5] Design the cyclic counter deﬁned in part (a) using the 7"one flip—flop per state”
approach with l) ﬂip—ﬂops. To obtain the output.) use a suitable standard combinational
module  do not design a gate networkl Show all connections. Show the initial state of this implementation. 5 3; *za , . S ‘ x a WWW l; , WWW”, 4 WWW W “ﬁpﬂ kmfip We iiiﬁgl "fig
gm" 2“ WV‘ i“ _ mmml Wm Wumme“mine/«WW:mw“' " ' ' w mwuw mm. if? «z
a
U3 v.
i "a MWMM a, l 1, , MWMMVW WWW ,
«Rwammw mm». ,,,..wmWWHWWMWMWW«r“WWW;WAWWWVM _ mmmuemmszuxmwm‘k‘wnmuww mam  Problem 4. (12 points) Design a hierarchical combinational network that ﬁnds the second
largest of four nonnegative integers A, B, (,7, 1). Each integer is reprenented by four bits. You may use only the following module types: 4 X 2—input multiplexer and lourrbit com
parator. The singlebit output of the comparator is 2. If the ﬁrst integer is larger than
the second, the output is z = 1. Otherwise, z 2 0. Deﬁne ﬁrst your basic module and
then design the network using your module. Indicate all inputs and connections on the
modules being used. m, not, Q; C 1M; A: 53% a.» ﬁx} l f Problem 5. (8 points) Implement the following systems using standard combinationai modules
(110 gate networks aﬂowed): Input: 3: E {07 1,273,4,5,6,7}, represented in binary by g; = {:vg,;171,m0},:m E {0; 1}.
OuLpuL: y E {0,1,2,3,4,5,6,7}, represented in binary by g 2 {3/2, y1,y0},y7; E {0,1}
Function: 3; : + mod 8 10 Problem 6. (13 points) a) [8 points] Complete the following table. If an entry in the table cannot be ﬁlled properly7
explain why and how to ﬁx it. Representation values are given in the decimal number system.
Number Number of Signed Representation Digit—vector
system digits n integer :L' value .7313 X
2’8 compl. 7 \Qt 116.31%
Ils’compl. 8 '\ 0349i C955; 2’s compL 9 100100110
2’s compl. 6 “= W /
i WM 1)) [5 points] Compute z : (1+ 21) — c in 2’s complement for a, : ~9, b : 17, and c z —77.
Perform calculations on bitweetors representing a, b and c and ShOW every step of your
work. How many bits should 2 have to represent the correct result? Check your work by
showing> for each step7 the corresponding values in decimal number system. m r“ T (gt? 5% mi mi ‘2 {3 {EM
fit rm, (2,, e} {fr«Wm {3;th.igmtwmtwglt t n. 11 Problem 7. (13 points) Design a sequential system speciﬁed by the following state transition
and output table using a modulo—8 counter with parallel load as the state register, a 8—to—1
multiplexer for the CNT input and NAND gates. Assume LD : CNT’. The design must take advantage of the count and parallel mode capabilities of the counter. Show a state
.W‘WWQ‘W if?“ M diagram and all your work. PS lnput Input
, 92.91% 55 = 0 1 ‘1? = 1
SO 000,0 001,0
51 ‘ 001 000,0 010,0
5’2 010 000,0 011,0
5'3 011 100,0 011,0 6/,
s4 100 101,0 001,0 3, 101 000,1 001,0 NS, 2 NS, 2 O
(D
Q 12 Problem 8. (10 points) Design a sequential system using combinationai and sequemiai stan—
dard modules that detects when :1:(/, — 7, L— 4.) < 13(1‘ — 3, 75), Where four—bit input sequences
are interpreted as positive integers. ...
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 Fall '07
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