Download Integer (and rational number)

Representing Rational Numbers
Binary numbering
16
1.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
8
0
4
0
2
1
1
1
1
32 16
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
8
4
2
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Representing Rational Numbers
2. Find the value of each of the binary expressions
(a) 10101012
(b) 11011012
(c) 11.011012
3. Find the binary and ternary representations of
(a) 1995 using both the remainder method and the subtraction method.
(b) 1996 using both the remainder method and the subtraction method.
(c) 0.25
(d) 0.2.
(e) 1/3.
4. Perform the indicated arithmetic
(a) 11012 × 101112
(b) 10012 × .12
(c) 100002 × 1.001012
(d) 11012 + 101112
(e) 10012 + 1011.12
(f) 10111002 − 1001012
5. Find the base -2 representation of each of the integers from 1 up to 30.
6. Find the factorial representation of each of the integers from 1 up to 30.
7. Find a Fibonacci representation of each of the integers from 1 up to 30.
8. An increasing sequence 1, 3, 4, 9, 10, 12, 13, . . . consists of all those positive integers which are powers of 3 or sums of distinct powers of 3. Fine the 100th
term of the sequence (where 1 is the first term, 3 is the second, etc.)
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Representing Rational Numbers
9. Each column in the table provides the representation of the numbers from 1
to 12 for a certain system of enumeration. Of course, the entries in column A
are decimal representations. Study the pattern, and determine the method of
representation. Then replace the ?’s with the appropriate representations.
A
B
C
1
0
1
2
1
10
3
10
100
4
2
101
100 1000
5
11 1001
6
7 1000 1010
3 10000
8
20 10001
9
10
101 10010
11 10000 10100
12 10101
12
?
?
13
?
?
14
?
?
15
16
?
?
?
?
17
?
?
18
D
1
10
11
20
21
100
101
110
111
120
121
200
?
?
?
?
?
?
E
1
2
10
11
12
20
21
22
100
101
102
110
?
?
?
?
?
?
F
1
110
111
100
101
11010
11011
11000
11001
11110
11111
11100
?
?
?
?
?
?
10. The floor of a real number x, denoted bxc is the largest integer that is not
bigger than x. The fractional part of a real number x, denoted hxi, is defined
by hxi = x − bxc. For example, 17 23 = b17 23 c + h17 23 i = 17 + 23 and −2 13 =
b−2 13 c + h−2 13 i = −3 + 23 . Solve simultaneously:
x + byc + hzi = 1.1
hxi + y + bzc = 2.2
bxc + hyi + z = 3.3
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