The remaining six digits are denoted by the symbols a

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Unformatted text preview: es of 16 single-character 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 day-today 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 vice-versa. 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.

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