Hexadecimal System In Computer

What Is the Hexadecimal System (Base-16)?


Computers speak binary (base-2), but long strings of 0/1 are hard for humans to read. Hexadecimal (base-16) gives a compact, human-friendly way to view the same bits: every 4 binary bits (a nibble) map to one hex digit. One byte (8 bits) maps neatly to 2 hex digits β€” perfect for memory dumps, colors, Unicode, and machine code.


πŸ”Ή 1️⃣ Decimal vs Binary vs Hexadecimal


  • Decimal (base-10): digits 0–9
  • Binary (base-2): digits 0–1
  • Hexadecimal (base-16): digits 0–9 + A, B, C, D, E, F (A=10 … F=15) 


Key 4-bit mapping:

ο»ΏπŸ”Ή 2️⃣ Why Hexadecimal?



  • Humans struggle with long binary strings (e.g., β€œI Love You!” in ASCII bits).
  • Hex compresses binary:
    • 11010100 β†’ D4
    • 1111 1111 1111 1111 1111 β†’ FFFFFF (grouped by 4 bits)
  • Each byte = 2 hex digits β†’ clean, readable dumps and color codes. 



πŸ”Ή 3️⃣ Hex Prefixes in Real Tech






πŸ”Ή 4️⃣ How Hexadecimal - Base-16 Works?

  • Base-2 Binary doubles: 1, 2, 4, 8, 16, 32, 64, 128 …

  • Base-16 Hexa powers:
    Hex digits multiply these powers by 0–15. 


πŸ”Ή 5️⃣ Convert Decimal β†’ Hex (division by 16 with remainders)



βœ… Example 1: 469 β†’ Hex


  • 469 Γ· 16 = 29, remainder 5 β†’ least-significant hex = 5
  • 29 Γ· 16 = 1, remainder 13 β†’ D
  • 1 Γ· 16 = 0, remainder 1 β†’ 1

Read remainders bottom→top: 1D5.


βœ… Example 2: 1513 β†’ Hex

ο»Ώ

  • 1513 Γ· 16 = 94, rem 9
  • 94 Γ· 16 = 5, rem 14 β†’ E
  • 5 Γ· 16 = 0, rem 5

Result: Read remainders bottom→top: 5E9.


βœ… Example 3: 479 β†’ Hex


  • 479 Γ· 16 = 29, rem 15 β†’ F
  • 29 Γ· 16 = 1, rem 13 β†’ D
  • 1 Γ· 16 = 0, rem 1

Result: Read remainders bottom→top: 1DF.


πŸ”Ή 6️⃣ Convert Hex β†’ Decimal (expand with powers of 16)


βœ… Example: 1D5₁₆ β†’ ?


βœ… Example: 5E9₁₆ β†’ ?



βœ… Example: 1DF₁₆ β†’ ?




πŸ”Ή 7️⃣ Convert Hex ↔ Binary (fastest method)

  • Hex β†’ Binary: replace each hex digit by its 4-bit binary:
    • D4 β†’ D=1101, 4=0100 β†’ 1101 0100.
  • Binary β†’ Hex: group bits in 4s from the right and map each group to one hex digit.


βœ… Example: 1D5₁₆ β†’ Binary?





πŸ”Ή 8️⃣ Convert Binary ↔ Hex (fastest method)



πŸ”— Interconnection

πŸ”Ή 4 bits ↔ 1 hex digit β†’ compact human view of binary.

πŸ”Ή 1 byte ↔ 2 hex digits β†’ easy memory/ASCII/color dumps.

πŸ”Ή Powers of 16 (1,16,256,4096…) β†’ drive decimal↔hex math.

πŸ”Ή Prefixes (#, 0x, &#, U+) β†’ tell tools to interpret as hex.

By mastering hex, you read/write low-level data confidently β€” firmware, encodings, colors, addresses β€” without drowning in 0/1. πŸš€ 


05 Programming Foundations - Hexa.pdf
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05 Programming Foundations - Hexa.pdf
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