3. The Octal Numbering System.

a. Unfortunately binary numbers tend to be long and cumbersome. Binary digits can be grouped

into sets of three or four to form octal (base 8 ) or hexadecimal (base 16) numbers respectively. The octal

numbering system uses only the digits zero through seven (base 8). The table in Figure 1-5 lists the

binary numbers zero through seven and their octal equivalents using the group of three method.

Group of Three Method.

b. The primary use of octal is in recording values stored in binary registers. There is a simple trick

for converting a binary number to an octal number. Simply group binary digits into groups of three

starting at the binary point, and read each set of three binary digits according to figure 1-5. This group of

three method of conversion is simple. It merely requires you to memorize the binary to octal conversions

from 0 to 7 to cover the octal radix of 8. For example, to convert the binary number 011101, we first

break it into threes (011 101). Then we convert each group of three binary digits, getting 35 in octal as a

result. Therefore, 0111012 = 358.

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