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Chabot College

Chabot College. ELEC 74A Hexadecimal Introduction. Hexadecimal Numbers. In the decimal (base 10) system, each digit has 10 possible values. In the hexadecimal (base 16) system, each digit has 16 possible values: Dec 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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Chabot College

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  1. Chabot College ELEC 74A Hexadecimal Introduction

  2. Hexadecimal Numbers In the decimal (base 10) system, each digit has 10 possible values. In the hexadecimal (base 16) system, each digit has 16 possible values: Dec 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Hex 0 1 2 3 4 5 6 7 8 9 A B C D E F

  3. Hexadecimal Numbering In decimal, each place value is a power of ten. We read the number 2342 as two-thousand three-hundred forty-two. 103 102 101 100 1000 100 10 1 2 3 4 2

  4. Hexadecimal Numbering In hexadecimal, each place value is a power of 16! We read the hex number 2342 as (2 x 4096) + (3 x 256) + (4 x 16) + (2 x 1) = 9026 163 162 161 160 4096 256 16 1 2 3 4 2

  5. Hexadecimal Notation Is 2342 a decimal or hex number? Hex numbers often • are preceded by 0x:0x2342 • are followed by h:2342h • include digits A - F:2B4C • used for MAC addresses:00-0A-3C-24-A2-99

  6. Conversions

  7. Hexadecimal Numbering In hex, each place value is a power of 16: 163 162 161 160 4096 256 16 1

  8. Hex to Decimal Conversion The hex number 2B1F is equivalent to 11,071 in decimal: 2 x 4096 = 8,192 B (11) x 256 = 2,816 3 x 16 = 48 F (15) x 1 = 15 Total = 11,071 163 162 161 160 4096 256 16 1 2 B 3 F

  9. Hex to Decimal Conversion Convert the hex number 04A3 to decimal: __ x 4096 = _____ __ x 256 = _____ __ x 16 = _____ __ x 1 = _____ Total = _____ 163 162 161 160 4096 256 16 1 0 4 A 3

  10. Hex to Decimal Conversion Convert the hex number 04A3 to decimal: 0 x 4096 = 0 4 x 256 = 1024 A (10) x 16 = 160 3 x 1 = 3 Total = 1187 163 162 161 160 4096 256 16 1 0 4 A 3

  11. Decimal to Hex Conversion The decimal number 1,442 is equivalent to 5A2 in hexadecimal: Convert 1,442: 1442 / 256 = 5 with remainder of 162 162 / 16 = 10 (A) with remainder of 2 2 / 1 = 2 Hex Answer: 5A2 163 162 161 160 4096 256 16 1 5 A 2

  12. Decimal to Hex Conversion Convert the decimal number 965 to hexadecimal: Convert 965: ___ / 256 = ___ with remainder of ___ ___ / 16 = ___ with remainder of ___ ___ / 1 = 2 Hex Answer: _____ 163 162 161 160 4096 256 16 1

  13. Decimal to Hex Conversion Convert the decimal number 965 to hexadecimal: Convert 965: 965 / 256 = 3 with remainder of 197 197 / 16 = 12 (C) with remainder of 5 5 / 1 = 5 Hex Answer: 3C5 163 162 161 160 4096 256 16 1 3 C 5

  14. Binary Review In binary, each place value is a power of two. Binary 1001 is equivalent to 9 in decimal. 23 22 21 20 8 4 2 1 1 0 0 1

  15. Hex to Binary Conversion • 16 = 24, so four binary bits can be represented as a single hex digit:

  16. Hex - Binary Relationship < 24 bits (OUI) > < 24 bits (station) > 0A-3C-19 24-C6-78 4 bits per hex digit 8 bits (one byte) per pair of hex digits 6 pairs of hex digits X 8 bits per pair = 48 bit MAC address

  17. Hex to Binary Conversion • Conversions are usually done one byte (8 bits) at a time. • Each byte is split into two 4-bit parts. • Each 4-bit part converts to one hex (24) digit:

  18. Hex to Binary Conversion Convert Hex C4 to Binary: • C = 1100 • 4 = 0100 • C4 = 11000100

  19. Hex to Binary Conversion Convert Hex 7F to Binary: • 7 = ____ • F = ____ • 7F = ________

  20. Hex to Binary Conversion Convert Hex 7F to Binary: • 7 = 0111 • F = 1111 • 7F = 01111111

  21. Binary to Hex Conversion Convert Binary 11000011 to Hex: • 1100 = _ • 0011 = _ • 11000011 = __

  22. Binary to Hex Conversion Convert Binary 11000011 to Hex: • 1100 = C • 0011 = 3 • 11000011 = C3

  23. Practice Slide Decimal < - > Hex 163 162 161 160 4096 256 16 1 Binary < - > Hex

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