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Unformatted text preview: ECE Scournow: 261 Name: Sp. 2007 1. EXAM 2
(Closed book, closed notes. You are allowed 2 singlesided sheets of notes. Show
your Work and write the answer in the space provided) Perform the following arithmetic operations: (24 prs.)
(a) 43+ (22) and
(b) 19 31
in binary using:
(i) 8bit signed 2’complement and
(ii) 8bit signed 1’s complement representation Cam,
) 43 OOIOIOII 22 OOOlOllO
 [IDIO‘IO
~22 [1101010 ﬁzz1
>45 OOOiOiOl (ZSCDMPL'EMEMT)
OO\
'Dlsexrvo _22_ H I OI
were! : 2, (its @ngmm)
('30 43 : oomxou
~21: [ilOiOO\
f
@«0 0mm ’0?
i
OOoloi0i 1’? 2—l
(B)({ [9: OOOlOOll 31 oootll\\ (fcbmgﬁmwﬂ
lllOOoO\
v31; lilooaol FM (3 EMW)
l Gom?L
3 3 @019 OOOiOOH
' wo g—‘L —3\‘. \[100000
If
11 Ill :00\\
W.————‘ 2. Design an adder that adds two 2bit numbers (A1 A0) and (B1 B0) and produces the
sum (82 SI 80) by going through the following steps:
(Note that the inputs to the adder are A1, A0, B1, BI) and the outputs are 82, 81, SO) a) Construct the tmth table for the adder. (10pm)
B1 E0 5 I A\‘"—'7 5L
A9 A 5'.
[8.47
Kg“? ~52: 812'Algi +AAOEU+AOK1K° (8 PISJ 3. a) Design a 3to~8line decoder with inputs A2, A1, A0 and outputs D0, D1, ....D7, by writing the equations for the outputs and then draw the circuit. (12 pts.)
A; "’"—" D4.
AI —
A—Q __ A54)“ Do
Al __,,__—‘
A1; b) Use the decoder you designed in part (a) to construct a S—to—llinc multiplexer with
inputs 10,11, 12, ...,I7, select inputs 82, SI, SO and output Y. (12pm) 4. A sequential circuit has 2 SR ﬂipﬂops A and B, one input X and one output Z. The inputs to the first ﬂipﬂop are S A and RA and its output is A. The inputs to the second flip ﬂop are $3 and RB and its output is B. the circuit is described by the following equations:
SA : B RA: BI .___...__
SB: AX+A’X’ = A 9 X
RB= AX’+A’X = Aex Z = A’B’X + AB’X’ + A’BX’ + ABX
(Notation: x’ denotes the complement of x) Derive the state table and state diagram of the circuit. (24 pts.)
"XT UT Pu
P1155347; men—L gl‘K(rg .l “SCFATE— O T
5mm: f ‘ 1.
A 3 5A RA A 55 i E 2— l
O
\OOOlOO‘
‘OloIOIO‘U
llO\QlO\oO
I‘llO\lOl
1/!
0/0
m
00 Ol
x/O ...
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 Fall '08
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