Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
1. Write each of the following Hindu Arabic numeral in expanded form:
a) 573
b) 9052
c) 7202
d) 72025
e) 1010102
2. Express each expanded form as Hindu- Arabic numeral.
a)
110   310    0 10   310   0 10   9 10 
b)
 7 10    4 10    6 10   9 10 
5
4
7
4
3
2
2
1
0
0
3. Complete the following table
BASE 10
BASE 2
BASE 5
BASE 8
BASE 12
BASE 16
736
10011101
321
7524
A1B
A1B
Note:
Base 12: A=10, B=11
Base 16: A=10 B=11 C=12 D=13 E =14 F=15
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
4. Complete the following table in the given base.
Addition Base 5
+
Multiplication Base 5
0
1
2
3
4
X
0
0
1
1
2
0
1
2
3
2
3
3
4
4
Multiplication Base 8
X
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
5. Complete the following table of conversions. Give the answer in the base of the rows. i.e.
row 1 in base seven, row 2 in base two, row 3 in base sixteen, etc.
Convert
to base
5seven
110two
ABsixteen
24five
276eight
10011two
24twelve
Seven
Two
Sixteen
Five
Eight
Twelve
Ten
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
6. Perform the indicated operations in the given base.
a) 22 four  13 four 
j)
b) 24twelve  17twelve 
k) 13 Atwelve  24twelve 
c) 34 five  24 five 
l)
d) 276eight  12eight 
m) 702eight  264eight 
e) 10011two  11100two 
n) 100110two  1010two 
f)
ABsixteen  BEsixteen 
1010 five  44 five 
o) 156sixteen  ACsixteen 
g) 542seven  4seven 
p) 3 four 223 four 
h) 1111two 11two 
i)
3132 four  2320 four 
q) 4 five 143 five 
D2sixteen  6 Asixteen 
r)
11two 1101two 
7. Indicate whether the following are true or false:
a) 2  4  mod 3
e) 105  100  mod 2 
i)
30  25  mod15
b) 3  4  mod 3
f)
19  9  mod 5
j)
11  25  mod 5
c) 15  4  mod11
g) 29  9  mod10 
d) 3  25  mod11
h) 2  29  mod15
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
8. For each problem fill in the blank with the right choice(s) from the given numbers. Some
number may be used more than once.

9

11

12

4

25

2

3

16

15

98
a) 2  4  mod__ 
e) __  5  mod11
b) 6  __  mod 3
f)
c) 12  9  mod__ 
g) 44  55  mod__ 
d) 49  9  mod__ 
h) 5  __  mod 3
100  55  mod__ 
i)
8  12  mod__ 
j)
112  __  mod10 
9. Construct an addition table for the 12-hr clock
10. Construct an addition table for the 7-hr clock
11. Construct a multiplication table for the 5-hr clock
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
Answers:
1.
a) 573  5 102  7 101  3 100
b) 9052  9 103  0 102  5 101  2 100
c) 7202  7 103  2 102  0 101  2 100
d) 72025  7 104  2 103  0 102  2 101  5 100
e) 1010102  1106  0 105  1104  0 103  1102  0 101  2 100
2.
a) 130309
b) 70040609
3.
BASE 10
BASE 2
BASE 5
BASE 8
BASE 12
BASE 16
736
1011100000
10421
1340
514
2E0
157
10011101
1112
235
111
9D
86
1010110
321
126
72
56
3924
111101010100
111144
7524
2330
F54
1463
10110110111
21323
2667
A1B
5B7
2587
101000011011
40322
5033
15B7
A1B
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
4. Note: Multiplication of different bases is achieved by converting the product of the numbers
to base five.
Ex: 2x3=6; 6 to base five is 11.
Addition Base 5
+
Multiplication Base 5
0
1
2
3
4
X
0
1
2
3
4
0
0
1
2
3
4
0
0
0
0
0
0
1
1
2
3
4
10
1
0
1
2
3
4
2
2
3
4
10
11
0
2
4
11
13
3
3
4
10
11
12
3
0
3
11
14
22
4
4
10
11
12
13
4
0
4
13
22
31
2
Multiplication Base 8
X
0
1
2
3
4
5
6
7
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
2
0
2
4
6
10
12
14
16
3
0
3
6
11
14
17
22
25
4
0
4
10
14
20
24
30
34
5
0
5
12
17
24
31
36
43
6
0
6
14
22
30
36
44
52
7
0
7
16
25
34
43
52
61
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
5.
The conversion of all the numbers to all of the given bases is:
Convert
to base
5seven
110two
ABsixteen
24five
276eight
10011two
24twelve
10
Seven
5
6
333
20
361
25
40
13
Two
101
110
10101011
1110
10111110
10011
11100
1010
Sixteen
5
6
AB
E
BE
13
1C
A
Five
10
11
1141
24
1230
34
103
20
Eight
5
6
253
16
276
23
34
12
Twelve
5
6
123
12
13A
17
24
A
Ten
5
6
171
14
190
19
28
10
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
6. Note: r stands for remainder
a) 101 four
b) 3Btwelve
c) 113 five
d) 310eight
e) 101111two
f)
169sixteen
g) 3131seven
h) 101101two
i)
57 F 4sixteen
j)
212 four
k) 116twelve
l)
411 five
m) 416eight
n) 11100two
o) AAsixteen
p) 32 four r 1 four
q) 22 five
r)
100two r 1two
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Contemporary Mathematics- MAT 130
7.
Numeration Systems (Chapter 4)
a) F
e) F
i)
F
b) F
f)
j)
F
c) T
g) T
d) T
h) F
a) 2
e) 16
i)
2, 4
b) 3, 9, 12, 15
f)
j)
2, 12
c) 3
g) 11
d) 2, 4
h) 2, 11, 98
T
8.
3, 9, 15
9.
+
0
1
2
3
4
5
6
7
8
9
10
11
0
0
1
2
3
4
5
6
7
8
9
10
11
1
1
2
3
4
5
6
7
8
9
10
11
0
2
2
3
4
5
6
7
8
9
10
11
0
1
3
3
4
5
6
7
8
9
10
11
0
1
2
4
4
5
6
7
8
9
10
11
0
1
2
3
5
5
6
7
8
9
10
11
0
1
2
3
4
6
6
7
8
9
10
11
0
1
2
3
4
5
7
7
8
9
10
11
0
1
2
3
4
5
6
8
8
9
10
11
0
1
2
3
4
5
6
7
9
9
10
11
0
1
2
3
4
5
6
7
8
10
10
11
0
1
2
3
4
5
6
7
8
9
11
11
0
1
2
3
4
5
6
7
8
9
10
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Contemporary Mathematics- MAT 130
Numeration Systems (Chapter 4)
10.
+
0
1
2
3
4
5
6
0
0
1
2
3
4
5
6
1
1
2
3
4
5
6
0
2
2
3
4
5
6
0
1
3
3
4
5
6
0
1
2
4
4
5
6
0
1
2
3
5
5
6
0
1
2
3
4
6
6
0
1
2
3
4
5
11.
X
0
1
2
3
4
0
0
0
0
0
0
1
0
1
2
3
4
2
0
2
4
1
3
3
0
3
1
4
2
4
0
4
3
2
1
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