and also here's a generic example that the LSB can matter even with *very* unbalanced multiplier input widths (pretend that this is a 2×40 -> 2-bit multiplication):
```
>>> hex(0x3 * 0x5555555555)
'0xffffffffff'
>>> hex(0x3 * 0x5555555556)
'0x10000000002'
```