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Codiode/Problems/Combinational Logic

Excess-3 Self-Complementing Property

MediumLogic CircuitAnalyze

Early arithmetic hardware utilized the excess-3 encoding scheme to perform decimal subtraction using simple bit inversion.

The excess-3 code represents a decimal digit d by adding 3 to its value before converting to a 4-bit binary sequence. A decimal 4 maps to 0111, and its nine's complement, decimal 5, maps to 1000.

Analyze the bit patterns for all decimal digits from 0 to 9 in excess-3. Determine the relationship between the logical bitwise complement of an encoded digit and the arithmetic nine's complement of that decimal digit.

Constraints

  • Decimal digits range strictly from 0 to 9.
  • The excess-3 encoding uses exactly 4 bits per digit.
  • Valid excess-3 codes range from 0011 to 1100.

Topics

arithmeticbcdexcess-3encoding

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