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L5, Hexadecimal System, What is Hexadecimal System?, package q10742

What is Hexadecimal System? 

The numbering system which uses base-16 is called Hexadecimal System or simply Hex. A base (also called radix) is the number of unique digits or symbols (including 0) used to represent a given number. In Hexadecimal System (base-16) a total of 16 symbols are used.
Digits 0(zero) to 9(Nine) are used to represent values from 0 to 9 respectively and alphabets ABCDE and F (or abcde and f) are used to represent values from 10 to 15 respectively.

In Java and many other programming languages 0x is used as a prefix to denote a hexadecimal representation.


For example, in hexadecimal the value of Zero is represented as 0x0, where

0 = (0 * 160) = (0 * 1)
Similarly 12 ...up to 9:
1 = (1 * 160) = (1 * 1)
2 = (2 * 160) = (2 * 1)
...
9 = (9 * 160) = (9 * 1)
10 = A = (10 * 160) = (10 * 1)
15 = F = (15 * 160) = (15 * 1)


Now, lets try representing Twenty One (21), remember we can use 0 to 9 and the alphabets A to F to represent 21, let us divide 21 by 16 and write down [quotient][reminder], i.e.: [1][5]

21 = 0x15 = (1 * 161) + (5 * 160) = (16) + (5)

Similarly, lets try representing One Hundred and Sixty (160), let us divide 160 by 16 and write down [quotient][reminder], i.e.: [10][0], [A][0] (since 10 is represented by A)
160 = 0xA0 = (10 * 161 + (0 * 160) = (160) + (0)

Similarly, lets try representing Three Thousand Four Hundred and Sixty (3460). Let us divide 3460 by 16 and write down [quotient][reminder], i.e.: [216][4], (216 divided by 16 is [13][8], which is represented as [D][8]). So 3460 is represented as 0xD84

3460 = 0xD84 = (13 * 162) + (8 * 161) + (4 * 160) = (13 * 256) + (8 * 16) + (4 * 1) = (3328) + (128) + (4)

In Java, both uppercase and lowercase letters can be used when representing Hex values. For example:
int hexHunderedAndSixty = 0xA0; // or 0Xa0, however 0xA0 is preferred
Select all the correct statements given below.
  • In Hexadecimal System, a base of 10 is used
  • Decimal 100 is equal to 0x64 in Hex
  • Hex value of 0xCAFE is equal to Decimal 51966
  • 0x0001 in Hex is equal to 0X1 in Hex and is equal to 1 in Decimal

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