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Codiode/Problems/Arithmetic

ALU Less Than Flag Logic

HardLogic CircuitBuild

Modern processors avoid dedicating silicon to standalone comparators. Instead, they evaluate branching conditions by performing a subtraction and analyzing the resulting condition flags.

Derive the signed Less Than (LT) condition for an instruction like CMP A, B using only the Negative (N) and Overflow (V) flags generated by the A - B operation. The output LT must assert when operand A is strictly less than operand B in two's complement representation.

| N | V | LT | |-----|-----|------| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |

Constraints

  • Combinational logic only.
  • Implement using basic logic gates.

Topics

arithmeticaluflagssigned-logic

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