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Understanding Binary System and Complements in Numeration

The binary system, based on 2 digits (0 and 1), serves as a positional numeration with various components like binary-to-decimal conversion, decimal-to-binary conversion, addition, multiplication, subtraction, and division. Additionally, the concept of complements, including decimal and binary complements like ones complement and twos complement, is crucial for operations. The use of nines complement and tens complement in subtraction is also highlighted for a comprehensive understanding of numerical computation.

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Understanding Binary System and Complements in Numeration

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  1. Prof. Dr. Abou-Hashema Mostafa

  2. The binary system is the positional numeration of base b = 2. Its two digits 0 and 1 are called bits for short. 20, 21, 22, 23(for integers) Binary System 2−3, 2−2, 2−1(for fractions)

  3. Binary to Decimal Conversion

  4. Binary to Decimal Conversion

  5. Decimal to Binary Conversion N = (109.78125)10 = ( )2 (109.78125)10 = (1101101.11001 )2

  6. Binary Addition

  7. Binary Multiplication

  8. Binary Subtraction

  9. Binary Division

  10. Complements • Decimal complements Nines complement Tens complement

  11. To illustrate the use of complement in subtraction Nines Complement Tens Complement

  12. • Binary complements Ones complement The ones complement of A is obtained by subtracting each digit of A from 1 Twos complement The twos complement of A is its ones complement plus 1 Complements

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