1. Data Storage Introduction to computer, 2nd semester, 2010/2011 Mr.Nael Aburas nras@iugaza.edu.psnras@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 0-9 10 are represented normally, but the numbers 10 10 through 15 10 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 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. 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 The following shows how to convert the hexadecimal number (1A) 16 to decimal = 1 × 16 1 + A × 16 0 =16 + 10 ×1 =16+10 = 26 convert (F4C) 16 to decimal = (F x 16 2 ) + (4 x 16 1 ) + (C x 16 0 ) = (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 (24C) 16 Each hexadecimal digit is converted to 4-bit patterns Each hexadecimal digit is converted to 4-bit patterns 2 → 0010, 4 → 0100, and C → 1100 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 (1256) 8

10. Octal to Decimal convert (632) 8 to decimal = (6 x 8 2 ) + (3 x 8 1 ) + (2 x 8 0 ) = (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 11100111 2 = 347 8 11000 010101010 010 001 2 = 3025221 8

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