Appendix - Some Useful Tables
1. Octal Multiplication Table
x
1
2
3
4
5
6
7
10
1
1
2
3
4
5
6
7
10
2
2
4
6
10
12
14
16
20
3
3
6
11
14
17
22
25
30
4
4
10
14
20
24
30
34
40
5
5
12
17
24
31
36
43
50
6
6
14
22
30
36
44
52
60
7
7
16
25
36
43
52
61
70
10
10
20
30
40
50
60
70
100
2. Powers of 2
n
2 n
n
2n
1
2
16
65 536
2
4
17
131 072
3
8
18
262 144
4
16
19
524 288
5
32
20
1 048 576
6
64
21
2 097 152
7
128
22
4 194 304
8
256
23
8 388608
9
512
24
16 777 216
10
1 024
25
33 554 432
11
2 048
26
67 108 864
12
4 096
27
134 217 728
13
8 192
28
268 435 456
14
16 384
29
536 870 912
15
32 768
30
1 073 741 824
3. Recurring Fractions in Binary
( 1 )/( 3 )
= 0.0̇ 1̇
( 1 )/( 5 )
= 0.0̇ 011̇
( 1 )/( 7 )
= 0.0̇ 01̇
( 1 )/( 9 )
= 0.0̇ 00111̇
( 1 )/( 11 )
= 0.0̇ 001011101̇
( 1 )/( 13 )
= 0.0̇ 00100111011̇
( 1 )/( 15 )
= 0.0̇ 001̇
( 1 )/( 17 )
= 0.0̇ 0001111̇
( 1 )/( 19 )
= 0.0̇ 00011010111100101̇
( 1 )/( 21 )
= 0.0̇ 00011̇
( 1 )/( 25 )
= 0.0̇ 0001010001111010111̇
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