Excess-3 Self-Complementing Property
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
0to9. - The excess-3 encoding uses exactly 4 bits per digit.
- Valid excess-3 codes range from
0011to1100.
Topics
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