1
EE 101 Midterm
Fall ’0
9
● Redekopp
Name: ___
Solutions
____________________
Lecture 9:30 / 12:30 / 2:00
Closed Book
Score: ________
No calculators
are allowed.
Show all your work to get full credit.
1.
(18 pts.) Number Systems & Arithmetic
(12 pts.)
a.
(6 pts.)
Represent
120
10
in the following systems w/ the given number of bits:
System
(show work for partial credit)
8bit Signed
Magnitude

64 + 32 + 16 + 8
= 1111 1000
8bit
2’s complement
= 128 + 8 = 1000 1000
16bit
2’s complement
(don’t work
too hard)
sign extend =>
1111 1111 1000 1000
b.
(4 pts.)
Represent 185
10
in the following bases:
System
(show work for partial credit)
8bit Unsigned
Binary
128 + 32 + 16 + 8 + 1 = 1011 1001
(Unsigned)
Hexadecimal
B9 hex
c.
(8 pts.)
Perform the indicated arithmetic operations given the representation systems
below to find the
8bit (not 9bit)
results. (Do not use the borrow method for subtraction,
use the 2’s complement method of subtraction.)
Show intermediate steps.
Finally,
state
whether overflow has occurred and briefly justify
why it has or has not occurred
.
a.) 2’s comp. system
b.) Unsigned binary
00111011
2
–
10000000
2
00111011
2
01111111
2
+
1
2
10111011
2
11110011
2
+
00110110
2
00101001
2
Overflow:
Y / N
Why?
P + P = N
Overflow:
Y / N
Why?
Final Cout = 1
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2
2.
(10 pts.) Short Answer
a.
How many 1bit wide, 2to1 muxes would be needed to build a 2bit wide, 6to1 mux.
1bit wide 6to1 mux requires 5 2to1 muxes.
to make it 2bits wide, replicate.
= 5 x 2 = 10
muxes
b.
A 2level NORAND circuit degenerates to what gate?
NOR gate
c.
True/
False
: An arbitrary, (singlebit output) logic function of
three
variables (e.g.
F(x,y,z) can
always
be implemented with
only
a 2to1 mux and a single inverter).
d.
A 1to31 demux requires a minimum of how many select bits?
5 bits
e.
In a ripplecarry adder (an adder made from chaining full adders), propagation delay is
proportional
to the individual full adder propagation delay of?
1.
The carryout bit of the full adders
2.
The sum bit of the full adders
3.
Neither.
Delay in a ripple carry adder is constant no matter how many full adders.
4.
Both a and b.
f.
Given a function of 5 variables A[4:0], write the algebraic form of minterm 25.
A4 and
A3 and A2’ and A1’ and A0
g.
What is
the 16’s complement of 5C
16
?
FF
–
5C = A3 + 1 = A4
h.
True / False:
Given a function, G,
of 4variables:
A,B,C,D that is implemented using a
4to1 mux whose 2 select bits are tied to A and B as shown below,
input
i1
of the mux should be connected to:
1.
G(1,0,C,D)
2.
G(0,1,C,D)
3.
C XOR D
4.
G(A,B,0,1)
Y
A B
S
1
S
0
I0
I1
I2
I3
G
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 Fall '06
 Redekopp
 pts, Input/output, 2bit adder

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