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Unformatted text preview: es of 16 singlecharacter digits or symbols. The first 10 digits are the digits of the
decimal number system  0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The remaining six digits are denoted
by the symbols A, B, C, D, E, and F representing the decimal values 10, 11, 12, 13, 14,
and 15 respectively. In the hexadecimal number system, therefore, the letters A through F
are number digits. The number A has a decimal equivalent value of 10 and the number F
has a decimal equivalent value of 15. Thus, the largest single digit is F or 15 (one less
than the base). Again, each position in the hexadecimal system represents a power of the
base (16). Thus the decimal equivalent of the hexadecimal number 1AF (written as
1AFI6) is:
(1 x 162) + (A x 161) + (F x 16°), or
(1x256)+ (10x16) 256+160+ 15, or 431
(15xl), or
Hence, 1AFI6 = 43110
Observe that since there are only 16 digits in the hexadecimal number system, 4 bits (2 4
=16) are sufficient to represent any hexadecimal number in binary.
CONVERTING FROM ONE NUMBER SYSTEM TO ANOTHER
Numbers expressed in decimal number system are much more meaningful to us than are
values expressed in any other number system. This is mainly because of the fact that we
have been using decimal numbers in our daytoday life right from childhood. However,
any number value in one number system can be represented in any other number system.
Because the input and the final output values are to be in decimal, computer professionals
are often required to convert numbers in other number systems to decimal and viceversa.
There are many methods or techniques that can be used to convert numbers from one
base to another. We will see one technique used in converting to base 10 from any other
base and a second technique to be used in converting from base 10 to any other base.
Converting to Decimal from Another Base
The following three steps are used to convert to a base 10 value from any other number
system:
Step 1: Determine the column (positional) value of each digit (this depends on the
position of the...
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This document was uploaded on 04/07/2014.
 Spring '14

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