Introduction to Computer Science
By:
Huong Nguyen
Introduction to Computer Science
By:
Huong Nguyen
Online:
< >
C O N N E X I O N S
Rice University, Houston, Texas
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•
•
•
•
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•
•
•
−
N
(b)
= a
n
a
n−1
a
n−2
a
1
a
0
a
−1
a
−2
a
−m
a
i
i
th
a
0
−
×
3
+ 2 ×
2
+ 4 ×
1
×
0
= 5 ×1000 + 2 ×100 + 4 ×10 + 6 ×1
254.68 = 2 ×10
2
+ 5 × 10
1
+ 4 × 10
0
+ 6 × 10
−1
+ 8 × 10
−2
= 200 + 50 + 4 +
6
10
+
8
100
11101.11
(2)
235.64
(8)
= 2 ×8
2
+ 3 × 8
1
+ 5 × 8
0
+ 6 × 8
−1
+ 4 × 8
−2
= 157.8125
(10)
34F 5C
(16)
= 3 ×16
4
+ 4 × 16
3
+ 15 × 16
2
+ 5 × 16
1
+ 12 × 16
0
= 216294
(10)
65
(8)
= 110 1012
17
(8)
= 001 1112
235.64
(8)
= 2 ×8
2
+ 3 × 8
1
+ 5 × 8
0
+ 6 × 8
−1
+ 4 × 8
−2
= 157.8125
(10)
d
n−1
d
n−2
d
2
d
1
d
0(10)
a
0
a
1
a
n−1
43868
(10)
>
>
43868.39625
(10)
•
•
•
•
•
•
•
•
•
• . . . . . .
• . . . . . .
• 2
n
− 1
•
•
•
•
×
×
×
×
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•
•
•
12.34 = 1 ∗10
1
+ 2 ∗ 10
0
+ 3 ∗ 10
−1
+ 4 ∗ 10
−2
101.1012 = 1 ∗2
2
+ 0 ∗ 2
1
+ 1 ∗ 2
0
+ 1 ∗ 2
−1
+ 0 ∗ 2
−2
+ 1 ∗ 2
2
= 4
(10)
+ 1
(10)
+ 0.5
(10)
+ 0.125
(10)
= 5.625
(10)
(−1)
s
d
0
· d
1
d
2
d
p−1
× b
e
•
• d
0
· d
1
d
2
d
p−1
≤ d
i
<
• e, e
min
≤ e ≤ e
max
•
·
·
· 00 00 00 00 00 0 × 2
−4
(−1)
s
d
0
· d
1
d
2
d
p−1
(−1)
s
d
0
+ d
1
b
−1
+ d
2
b
−2
d
−1
b
(p−1)
b
e
• e
max
•
•
•
•
• e
min
127
(10)
− 126
(10)
= 1 =
00000001
(2)
e
max
127
(10)
+ 127
(10)
= 254
(10)
= 11111110
(2)
• 1.d
1
d
2
d
23
•
• 2 × 2
127
∼
=
3.402823 × 10
38
• 1 × 2
−127
∼
=
1.17549 × 10
−38