c. There are several other shortcuts for converting octal to decimal and decimal to octal, manually

and using tables. Once you have converted the number to binary you can then convert to decimal or octal

from depending on what base you are converting from. Tables are as convenient as any other method.

Octal-to-decimal-to-octal tables are readily available in the military or commercial manuals for specific

computers. An important use for octal is in listing of programs and for memory dumps for binary

machines, thus making printouts more compact. In keeping track of the contents of registers and in orally

conveying the contents of a register to someone, it is very useful to use octal characters rather than binary.

000 001 0002

4. The Hexadecimal Numbering System.

a. General. The hexadecimal system, often referred to as hex, is a base 16 number system. The

symbol used in the hexadecimal system are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

b. Hexadecimal Conversion. All the IBM 360 series of machines have their memories organized

into sets of bytes (a byte consists of eight binary digits). Each byte either is used as a single entity to

represent a single alphanumeric character (a combination of letter and numbers) or is broken into two

four-bi pieces. The group of four method is another shortcut for converting binary to hexadecimal, and

the reverse. This method is based on the equivalency of any four-bit binary group to a particular

hexadecimal digit as shown in figure 14.

(1) For binary-to-hexadecimal conversions, the binary number is divided into four-bit groups,

beginning at the radix point; the hexadecimal equivalent of each group is then written.