Converting Decimal to Hexadecimal

Overview

• Decimal number system is base 10 (digits 0-9).
• Hexadecimal number system is base 16 (digits 0-9 and letters A-F).

Hexadecimal Correspondences

• Decimal to Hexadecimal conversions:
  • 0 = 0
  • 1 = 1
  • 2 = 2
  • 3 = 3
  • 4 = 4
  • 5 = 5
  • 6 = 6
  • 7 = 7
  • 8 = 8
  • 9 = 9
  • 10 = A
  • 11 = B
  • 12 = C
  • 13 = D
  • 14 = E
  • 15 = F

Conversion Process

Using a Calculator

1. Example 1: Convert 479

   • Divide 479 by 16 → 29.9375
   • Integer part: 29, Remainder: 15 (F)
   • Divide 29 by 16 → 1.8125
   • Integer part: 1, Remainder: 13 (D)
   • Divide 1 by 16 → 0.0625
   • Integer part: 0, Remainder: 1
   • Result: 479 = 1DF (base 16)

2. Example 2: Convert 894

   • Divide 894 by 16 → 55.875
   • Remainder: 14 (E)
   • Divide 55 by 16 → 3.4375
   • Remainder: 7
   • Divide 3 by 16 → 0.1875
   • Remainder: 3
   • Result: 894 = 37E (base 16)

Without a Calculator (Long Division)

1. Example 3: Convert 3284

   • 3284 ÷ 16 → 205 remainder 4
   • 205 ÷ 16 → 12 remainder 13 (D)
   • 12 ÷ 16 → 0 remainder 12 (C)
   • Result: 3284 = CD4 (base 16)

2. Example 4: Convert 7956

   • 7956 ÷ 16 → 497 remainder 4
   • 497 ÷ 16 → 31 remainder 1
   • 31 ÷ 16 → 1 remainder 15 (F)
   • 1 ÷ 16 → 0 remainder 1
   • Result: 7956 = 1F14 (base 16)

3. Example 5: Convert 14259

   • Using calculator:
     • 14259 ÷ 16 → 891 remainder 3
     • 891 ÷ 16 → 55 remainder 11 (B)
     • 55 ÷ 16 → 3 remainder 7
     • 3 ÷ 16 → 0 remainder 3
     • Result: 14259 = 37B3 (base 16)
   • Without calculator:
     • 14259 ÷ 16 → 891 remainder 3
     • 891 ÷ 16 → 55 remainder 11 (B)
     • 55 ÷ 16 → 3 remainder 7
     • 3 ÷ 16 → 0 remainder 3
     • Result: 14259 = 37B3 (base 16)

Conclusion

• Understanding both methods of conversion is essential for handling decimal to hexadecimal transformations efficiently.