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Number Systems

Decimal | Binary | Hexadecimal. Number Systems. Revision Introductory Lesson. In this topic …. Decimal System. Binary System. Hexadecimal System. Conversions. Conversions …. Decimal  Binary. Binary  Decimal. Binary  Hexadecimal. Decimal  Hexadecimal. Hexadecimal  Binary.

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Number Systems

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  1. Decimal | Binary | Hexadecimal Number Systems Revision Introductory Lesson

  2. In this topic … Decimal System Binary System Hexadecimal System Conversions

  3. Conversions … Decimal  Binary Binary  Decimal Binary  Hexadecimal Decimal  Hexadecimal Hexadecimal  Binary

  4. Decimal System • Ten fingers • Ten different numbers possible: • 0 1 2 3 4 5 6 7 8 9 • Base 10 e.g. 654210

  5. Our Number System 6 5 4 2 6 5 4 2 100 = 1x 2 = 2 101= 10 x 4 = 40 102= 100 x 5 = 500 103= 1000 x 6 = 6000 + 6542 tens units hundreds thousands … 104103102 101100 … 10000 1000 100 10 1

  6. Binary System • Switch • Two possible values:0 and 1 • Base 2E.g. 011101012

  7. Binary System … 27 26 25 242322 2120 … 128 64 32 16 8 4 2 1 0 1 1 1 0 1 0 1 MSB LSB Most Significant Bit Least Significant Bit The bit position having the greatest value The bit position having the least value

  8. Binary to Decimal Conversion Q: Convert 011101012 to decimal. A: 128 64 32 16 8 4 2 1 0 1 1 1 0 1 0 1 Add together the corresponding values where there is a 1 64 + 32 + 16 + 4 + 1 = 11710

  9. Decimal to Binary Conversion Method 1 – Using Long Division • Q: Convert 1810 to binary: A: 2 18 2 9 r 0 1810 = 0100102 2 4 r 1 2 2 r 0 2 1 r 0 0 r 1

  10. Decimal to Binary Conversion • Method 2 – Using Weights Q: Convert 17310 to binary. A: 128 64 32 16 8 4 2 1 1 0 1 0 1 1 0 1 2 Working: 173 – 128 45 – 32 1 – 1 5 – 4 13 – 8 5 0 45 13 1

  11. Any Questions?

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