1) Number representation (15 pts)
a) For each binary vector below, what does it represent as an Octal number and a Hexadecimal
number?
Binary
Octal
Hexadecimal
10110011
263
B3
01111100
174
7C
11111111
377
FF
b) Given
X
and
Y
below that are 5bit numbers in 2’s complement form, fill in the table of what
S
should be bitvector form (
even if the result causes an overﬂow
). Indicate whether or not
there is an
overﬂow
and what
S
is as a number (if
S
results in an overﬂow, then just put an ”x”
under the
S
column). (First two rows provide examples.)
X
Y
S
=
X
−
Y
S
as a
x
4
x
3
x
2
x
1
x
0
y
4
y
3
y
2
y
1
y
0
s
4
s
3
s
2
s
1
s
0
Overﬂow?
number
11101
00011
11010
no
6
00001
00111
11010
no
6
01000
10010
10110
yes
x
10111
10111
00000
no
0
10111
01011
01100
yes
x
01100
00101
00111
no
7
10101
10111
11110
no
2
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2) Multilevel logic minimization (10 pts)
Given following logic equations, minimize the number of literals, e.g. by using common subexpres
sions, Boolean rules, etc. You can introduce new immediate equations for common subexpressions
if it helps to reduce the number of literals. Put a box around your final answer, and indicate the
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '06
 Rosing
 Binary numeral system, Xi Zi, ci Bi

Click to edit the document details