Floating Point Exception Flags
Floating-point units must flag special numerical cases immediately to prevent processor pipeline stalls or silent data corruption. These exception flags inform the control logic when an arithmetic operation results in infinity, zero, or an invalid number.
The circuit receives a 4-bit exponent E and a 4-bit mantissa M. The output flags must assert under specific conditions derived from standard floating-point behavior: * is_zero is 1 when both E and M are strictly zero. * is_inf is 1 when E is at its maximum value (all ones) and M is zero. * is_nan is 1 when E is at its maximum value and M contains at least one non-zero bit.
| E | M | is_zero | is_inf | is_nan | |-----|-----|-----------|----------|----------| | 0000| 0000| 1 | 0 | 0 | | 0000| 0001| 0 | 0 | 0 | | 1111| 0000| 0 | 1 | 0 | | 1111| 0001| 0 | 0 | 1 | | 1000| 0000| 0 | 0 | 0 |
Constraints
- Implement using only combinational logic.
- Do not use high-level comparison blocks: build the detection logic using primitive logic gates.
Topics
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