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CS 70
Discrete Mathematics for CS
Spring 2005
Clancy/Wagner
HW 6
Due Thursday, March 10
Coverage:
This assignment involves topics from the lectures of February 22 and 24 and March 1, and
from Rosen sections 2.2, 2.4, 2.5, and pages 181185 in section 2.6.
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Homework exercises:
1. (14 pts.)
Radix –2
Radix

2
representation
is analogous to radix 2 (binary) representation. An integer
n
is represented
as
d
k
d
k

1
···
d
1
d
0
if
n
=
d
k
(

2
)
k
+
d
k

1
(

2
)
k

1
+
...
d
1
(

2
)
1
+
d
0
(

2
)
0
and all the
d
j
are 0 or 1.
(a) What’s the radix

2 representation of 9?
(b) Prove that every integer
n
>
0 can be represented in radix

2.
(c) Is the representation unique? That is, can every integer
n
>
0 be represented in
exactly one way
in radix

2? Prove the claim, or display a counterexample.
2. (14 pts.)
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This note was uploaded on 09/03/2011 for the course CS 70 taught by Professor Papadimitrou during the Fall '08 term at University of California, Berkeley.
 Fall '08
 PAPADIMITROU

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