Computer Science XI

Hexadecimal Number System

Hexadecimal representation of numbers is more efficient in digital applications because it occupies less memory space for storing large numbers. A hexadecimal number is represented using base 16. Hexadecimal or Hex numbers are used as a shorthand form of binary sequence. This system is used to represent data in a more compact manner. In the hexadecimal number system, the binary digits are grouped into sets of 4 and each possible combination of 4 binary digits is given a symbol as
follows: 0000 = 0 1000 = 8 0001 = 1 1001 = 9 0010 = 2 1010 = A 0011 = 3 1011 = B 0100 = 4 1100 = C 0101 = 5 1101 = D 0110 = 6 1110 = E 0111 = 7 1111 = F Since 16 symbols are used, 0 to F, the notation is called hexadecimal. The first ten symbols are the same as in the decimal system, 0 to 9 and the remaining six symbols are taken from the first six letters of the alphabet sequence, A to F. The
hexadecimal sequence 2C16 has the decimal equivalent: 2C16 = 2 x 161 + c x 160 = 32 + 12 = 4410 The hexadecimal representation is more compact than binary representation. It is very easy to convert between binary and hexadecimal systems. Each hexadecimal digit will correspond to four binary digits because 24 = 16. The hexadecimal equivalent of the binary sequence 1100100111012 is: 1100 1001 1101 = C9D16 C 9 D

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