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1
EE 101 Sample Midterm
Redekopp
Name:_________________________________________________________________
Score:
/ 100
1.
Short Answer
(5 pts.)
a.
What range of numbers can be represented with a 6bit 2’s complement system?
2
n1
to +2
n1
1 = 32 to +31
b.
What determines the speed of a digital circuit as discussed in class?
Levels/Stage of Logic (Number of inputs to a gate is also acceptable)
c.
Given a 5to32 decoder with inputs (A4, A3, A2, A1, A0), write out the logic equation
for output 17 (i.e. O17)?
17 = 10001
2
= A4 •A3’ •A2’ •A1’ •A0
d.
NANDOR logic implementations degenerates to what gate?
NAND
e.
A 20to1 mux would require a minimum of how many select bits?
5 bits
2.
For the decimal numbers below, convert to the indicated representation systems.
a.
(107)
10
= (?)
8bit 2’s comp.
= (?)
16’s comp.
(i.e. just conv. 2’s comp. value to hex)
(4 pts.)
107 = 10010101
2’s comp
= 95
16’s comp
b.
(59)
10
= (?)
8bit signed magnitude
(2 pts.)
59 = 10111011
8bit signed mag.
c.
235
10
= (?)
8
= (?)
BCD
(6 pts.)
235 / 8
= 29 r. 3
29/8
= 3
r. 5
3/8
= 0
r. 3
= 353
8
235 = 0010 0011 0101
BCD
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3.
Find the simplest SOP form of the following logic equation.
(8 pts.)
C
AB
C
C
A
B
C
A
F
+
•
+
+
•
+
=
]
)
(
)
[(
F
= ((AC’)+B)((AC’)+C) + ABC’
DeMorgan’s
= AC’ + BC + ABC’
T8’
= AC’ + BC
SingleVariable Theorems
(T1)
X + 0
= X
(T1’)
X • 1 = X
(Identities)
(T2)
X + 1 = 1
(T2’)
X • 0 = 0
(Null elements)
(T3)
X + X = X
(T3’)
X • X = X
(Idempotency)
(T4)
(X’)’ = X
(Involution)
(T5)
X + X’ = 1
(T5’)
X • X’ = 0
(Complement)
Two and ThreeVariable Theorems
(T6)
X +Y = Y + X
(T6’)
X • Y = Y • X
(Commutativity)
(T7)
(X+Y)+Z = X+(Y+Z)
(T7’)
(X•Y) •Z = X• (Y•Z)
(Associativity)
(T8)
X•(Y+Z) = X•Y + X•Z
(T8’)
X+(Y•Z) = (X+Y) • (X+Z)
(Distributivity)
(T9)
X + X•Y = X
(T9’)
X • (X + Y)
= X
(Covering)
(T10)
X•Y + X•Y’ = X
(T10’)
(X+Y) • (X+Y’) = X
(Combining)
(T11)
X•Y+X’•Z+Y•Z =
X•Y+X’Z
(T11’)
(X+Y)•(X’+Z)•(Y+Z) =
(X+Y)•(X’+Z)
(Consensus)
DeMorgan’s Theorem
(X • Y)’ = X’ + Y’
(T6’)
(X +Y)’ = X’ • Y’
(DeMorgan’s)
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 Fall '06
 Redekopp

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