OCTAL AND HEXADECIMAL NUMBER CONVERSION -2
Table 3-1 lists a few octal numbers and their representation in registers in binary-coded form. The binary code is obtained by the procedure explained above. Each octal digit is assigned a 3-bit code as specified by the entries of the first eight digits in the table.Similarly, Table 3-2 lists a few hexadecimal numbers and their representation in registers in binary-coded form. Here the binary code is obtained by assigning to each hexadecimal digit the 4-bit code listed in the first 16 entries of the table.
Comparing the binary-coded octal and hexadecimal numbers with their binary number equivalent we find that the bit combination in all three representations is exactly the same. For example, decimal 99, when converted to binary, becomes llOOOII. The binary-coded octal equivalent of decimal 99 is 001 100 Oll and the binary-coded hexadecimal of decimal 99 is 0110 OOll. If we neglect the leading zeros in these three binary representations, we find that their bit combination is identicaL This should be so because of the straightforward conversion that exists between binary numbers and octal or hexadecimaL The point of all this is that a string of 1's and O's stored in a register could represent a binary number, but this same string of bits may be interpreted as holding an octal number in binary-coded form (if we divide the bits in groups of three) or as holding a hexadecimal number in binary-coded form (if we divide the bits in groups of four).
The registers in a digital computer contain many bits. Specifying the content of registers by their binary values will require a long string of binary digits. It is more convenient to specify content of registers by their octal or hexadecimal equivalent. The number of digits is reduced by one-third in the octal designation and by one-fourth in the hexadecimal designation. For example, the binary number 1111 1111 1111 has 12 digits. It can be expressed in octals as 7777 (four digits) or in hexadecimal as FFF (three digits). Computer manuals invariably choose either the octal or the hexadecimal designation for specifying contents of registers.