octal numbers
Years ago, computers used octal numbers for representing binary numbers. Using octal numbers allows the reading of large binary numbers by breaking the
binary number into groups of three. This speeded up the entering and reading of binary numbers from a computer, thus resulting in reduced error.
Figure 41-2 shows octal numbers with their decimal and binary equivalents. The advantage is that octal numbers are converted directly from 3 bits of binary numbers. The octal number system is referred to as base 8. There are only eight digits (0–7) and then it recycles like the decimal system (0–9).
To convert binary to an octal number requires dividing the binary number into groups of three, starting from the right, as shown by the following example:
EXAMPLE:
Binary number 1001010011100001110102 Separate into groups of three:
100 101 001 110 000 111 0102
Convert to octal: 100 101 001 110 000 111 0102
Octal equivalent is: 45160728
To convert an octal number to a binary equivalent
requires reversing the process and converting the octal number to binary groups of three, as shown by the following example:
EXAMPLE:
Octal number: 16720548
Separate the numbers: 1 6 7 2 0 5 48
Convert to binary: 001 110 111 010 000 101 1002
Binary equivalent: 0011101110100001011002
Lead zeros can be dropped resulting in:
11101110100001011002
Like binary numbers, each octal number is a weighted number with a place value. The value of an octal number can be determined by adding the product of each digit and its place value. Figure 41-3 shows octal place values. The method for converting an octal number to a decimal is shown by the following example:
To convert a decimal number to an octal equivalent requires dividing the number by eight, as shown by converting 238210 to an octal number in the following example:
