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NUMBER SYSTEM AND CODES

5. NUMBER SYSTEM AND CODES. LEACH, MALVINO & SAHA. Why binary numbers are used. Almost all digital computers and systems are based on binary (two-state) operation. For instance, the switch shown in figure can be open or closed; therefore, a switch is one example of a natural binary device.

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NUMBER SYSTEM AND CODES

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  1. 5 NUMBER SYSTEM AND CODES LEACH, MALVINO & SAHA

  2. Why binary numbers are used • Almost all digital computers and systems are based on binary (two-state) operation. For instance, the switch shown in figure can be open or closed; therefore, a switch is one example of a natural binary device. Transistor ckt switch Tape rec. Disk drive

  3. Binary-to-Decimal Conversion • Positional notations and weights • Binary Weights • Streamlined Method • Fractions • Mixed Numbers

  4. Decimal-to-binary Conversion • Double Dabble • Fractions • Useful Equivalents

  5. Octal Numbers • Octal-to-Decimal Conversion • Decimal-to-Octal Conversion • Fractions • Octal-to-Binary Conversion • Binary-to-Octal Conversion

  6. Hexadecimal Numbers • Hexadecimal-to-Binary Conversion • Binary-to-Hexadecimal Conversion • Hexadecimal-to-Decimal Conversion • Decimal-to-Hexadecimal Conversion

  7. OTHERS • The ASCII Codes • The Excess-3 Code • The Gray Code

  8. Others • Gray Code • The advantage of such coding will be understood from this example • The disadvantage with gray code is that it is not good for arithmetic operation. Object moving along a track with sensors (a) binary coded and (b) gray coded. (a)Binary to Gray converter and (b)Gray to Binary converter

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