Service manual

STP 11-25R13-SM-TG
Q - 18
(13) Converting a large binary number directly to decimal can be time-consuming. Using the octal
system, the conversion to decimal is more rapid because there are fewer digits in an octal number. The
octal number system is often used in input-output units of a digital computer, while the computer still uses
binary to perform its calculations.
(14) The next conversion to cover is the decimal to octal number. Use the same method used in
the decimal to binary conversion. Divide the decimal number by the base number 8. The remainder is
the equivalent octal digit. Repeat this process until the quotient is zero. Write the octal number
horizontally left to right, starting with the bottom digit.
(15) The following example shows the conversion of decimal number 8965 to its octal equivalent.
Remainder
8 8965
8 1120 5
8 141 0
8 17 4
8 2 1
8 0 2
The octal equivalent of 8965
10
equals 21405
8
.
g. The Hexadecimal System (Conversion). The hexadecimal number system is generally used for
the same reason the octal system was used; that is, to simplify large binary numbers.
(1) Hexadecimal, as the name implies, has a base of 16. The 16 separate symbols used are 0-9
and A-F. The comparison between decimal, binary, and hexadecimal numbers is shown in Table Q-12.
The letter A in the hexadecimal system is equal to decimal 10, letter B equals decimal 11, and so forth.
Table Q-12. Relationship of Decimal, Binary, and Hexadecimal Numbers
(2) Now, how do we find the hexadecimal equivalent of a binary number? Starting at the decimal
point, arrange the binary into groups of four. Why four? Remember, there are 16 different combinations
of four binary bits, each corresponding to a hexadecimal digit.
Decimal Binary Hexadecimal
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A