The document discusses the octal numeral system which uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. It is a base-8 system where each place value has a multiplying power of 8. To count in octal, you increment the rightmost digit until it reaches 7 and then increase the next digit to the left by 1, repeating as needed. An example shows converting the octal number 15678 to its decimal equivalent of 887 by multiplying each digit by its place value.

1. Octal
• Eight digits: 0, 1, 2, 3, 4, 5, 6, 7
• Octal is base 8
• Positional numeral system
– The position of the symbol specifies the multiplier (as a power of 8)
• Counting
– Go through all the symbols in one position, increment the symbol in
the next highest position, repeat.

2. Octal
Octal Dec
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
Octal Dec
10 8
11 9
12 10
13 11
14 12
15 13
16 14
17 15
Octal Dec
20 16
21 17
22 18
23 19
24 20
25 21
26 22
27 23

3. Octal
• Number: 15678
Position 3 2 1 0
Multiplier 83 = 512 82 = 64 81 = 8 80 = 1

183
  5 82
  6 81
  7 80
 
512 320 48 7
 887