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Introduction to Hexadecimal and Octal Number Systems in Computer Data Storage

This document provides a comprehensive introduction to the hexadecimal and octal numbering systems, crucial for understanding computer data storage. It covers the basics of hexadecimal as a Base 16 system, its equivalent decimal conversions, and how to represent large binary strings efficiently. The document also explores the octal numbering system, its conversion methods to decimal, and binary representations. The information is tailored for students in the Faculty of Information Technology at the Islamic University of Gaza.

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Introduction to Hexadecimal and Octal Number Systems in Computer Data Storage

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  1. Data Storage Introduction to computer, 2nd semester, 2010/2011 Mr.NaelAburasnras@iugaza.edu.ps Faculty of Information Technology Islamic University of Gaza

  2. Hexadecimal (Hex) • Hex is a numbering system that uses Base 16. The numbers 0-910 are represented normally, but the numbers 1010 through 1510 are represented by the letters A through F • 1 hex digit is equivalent to 4 bits • Numbers are 0,1,2…..8,9, A, B, C, D, E, F. • The following shows that the number (2AE)16 in hexadecimal is equivalent to 686 in decimal. • The equivalent decimal number is N = 512 + 160 + 14 = 686.

  3. Hexadecimal (Hex) • Using hexadecimal, a very large binary string of 1s and 0s can be represented with just a few hexadecimal numbers by breaking the binary number into groups of four and then using the hexadecimal equivalent; for example, 1101100101001111 can be written as 1101 1001 0100 1111

  4. Hexadecimal to decimal • The following shows how to convert the hexadecimal number (1A)16 to decimal = 1 × 161 + A × 160 =16 + 10 ×1 =16+10 = 26 convert (F4C)16 to decimal = (F x 162) + (4 x 161) + (C x 160) = (15 x 256) + (4 x 16) + (12 x 1)

  5. Decimal to hexadecimal convert (4768)10 to hex. = 4768 / 16 = 298 remainder 0 = 298 / 16 = 18 remainder 10 (A) = 18 / 16 = 1 remainder 2 = 1 / 16 = 0 remainder 1 Answer: 1 2 A 0

  6. Hexadecimal to binary • (24C)16 • Each hexadecimal digit is converted to 4-bit patterns • 2 → 0010, 4 → 0100, and C → 1100 • (306 ) = (00110000 0110)

  7. Binary to hexadecimal Convert (010011100010)2 to hexadecimal ? We first arrange the binary number in 4-bit patterns: 0100 1110 0010 4 E 2 Convert (0010110001101011)2 to hexadecimal? 0010 1100 0110 1011 2 C 6 B

  8. Octal • The Octal numbering system is similar to the Hexadecimal numbering system. • This big difference is that the maximum value for Octal is 7 since it is Base 8 • 1 octal digit is equivalent to 3 bits.

  9. Octal • (1256)8

  10. Octal to Decimal • convert (632)8 to decimal = (6 x 82) + (3 x 81) + (2 x 80) = (6 x 64) + (3 x 8) + (2 x 1) = 384 + 24 + 2 = (410)10

  11. Decimal to Octal • convert (177)10 to octal 177 / 8 = 22 remainder is 1 22 / 8 = 2 remainder is 6 2 / 8 = 0 remainder is 2 Answer = 2 6 1

  12. Binary to octal • 111001112 = 3478 • 11000 010101010 010 0012 = 30252218

  13. Octal to binary • convert (632)8 to binary (110011010)2

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