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Understanding Number Systems: Decimal, Binary, Octal, and Hexadecimal

This guide explores various number systems essential in computer science, including decimal, binary, octal, and hexadecimal systems. Each system is broken down with practical examples, demonstrating how to convert between them. For instance, the binary number (11010)₂ converts to (26)₁₀ in decimal, and the octal number (127.4)₈ is equivalent to (87.5)₁₀. Additionally, hexadecimal representation is explained, detailing digits and letters from A to F. Knowledge of these systems is crucial for computing and programming.

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Understanding Number Systems: Decimal, Binary, Octal, and Hexadecimal

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  1. Number Sysytems D. W. ChathurikaPavithrani UvaWellassa University

  2. Number Systems • 724.5 = 7* 102 + 2*101 + 4*100 +5* 10-1

  3. Numbers Systems used in Computer Work • Decimal • Binary • Octal • Hexadecimal

  4. Binary • (11010)2 = 1*24 + 1*23 +0*22 + 1*21 + 0*220= (26) 10

  5. Octal • (127.4)8 = 1*82 + 2*81 + 7*80 + 4*8-1= (87.5)10

  6. Hexadecimal • First 10 digits from the decimal system • And the letters • A – 10 • B – 11 • C – 12 • D – 13 • E – 14 • F - 15

  7. Hexadecimal • (B65F)16 = 11*163 + 6*162 + 5*161 + 15*160 = (46687)10

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