Number System Conversion

Rumman Ansari Software Engineer 2025-05-11 03:37:16 312 Share
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✅ Number System Conversion Chart

There are 12 possible conversions among the four number systems:

From \ To	Binary	Octal	Decimal	Hexadecimal
Binary	—	✅ Binary → Octal	✅ Binary → Decimal	✅ Binary → Hex
Octal	✅ Octal → Binary	—	✅ Octal → Decimal	✅ Octal → Hex
Decimal	✅ Decimal → Binary	✅ Decimal → Octal	—	✅ Decimal → Hex
Hexadecimal	✅ Hex → Binary	✅ Hex → Octal	✅ Hex → Decimal	—

Uses base 10. Digits range from 0 to 9.

Example: (1024)₁₀ = 1×10³ + 0×10² + 2×10¹ + 4×10⁰ = 1024

Uses base 2. Digits are 0 and 1.

Example: (1101)₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13

Uses base 8. Digits range from 0 to 7.

Example: (658)₈ = 6×8² + 5×8¹ + 8×8⁰ = 432

Uses base 16. Digits range from 0–9 and A–F.

Example: (1A5C)₁₆ = 1×16³ + 10×16² + 5×16¹ + 12×16⁰ = 6748

Decimal to Binary: Divide by 2 and read remainders bottom to top.

Binary to Decimal: Multiply each bit by 2ⁿ from right to left.

Decimal to Octal/Hex: Same method, but divide by 8 or 16 instead.

Binary to Octal/Hex: Group binary digits (3 for octal, 4 for hex), then convert.