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Codiode/Problems/Combinational Logic

Two's Complement Shortcut: Rightmost-1 Rule

MediumLogic CircuitAnalyze

Hardware engineers reading hex dumps or debugging ALUs rely on fast mental math to decode negative binary values. The standard two's complement algorithm of inverting bits and adding one is computationally sound but slow for human inspection. A faster method exists: scanning from right to left, copying all bits up to and including the first 1, and then inverting all subsequent bits to the left.

The base value is the decimal number 96.

Apply the rightmost-1 shortcut to convert the 8-bit binary representation of 96 into -96. Identify the boundary bit where the inversion begins and determine the final 8-bit pattern.

Constraints

  • Assume 8-bit two's complement representation.
  • Binary representations must include all leading zeros.
  • Bit indices are zero-based, with index 0 representing the least significant bit (LSB).

Topics

twos-complementbinary-arithmeticdigital-foundations

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