Processing circuitry performs a processing operation to generate a two's complement result value representing a positive or negative number in two's complement representation. Normalization-and-rounding circuitry converts the two's complement result value to a normalized-and-rounded floating-point result value represented using sign-magnitude representation. The normalization-and-rounding circuitry comprises incrementing circuitry to perform an increment addition (e.g. a rounding increment or a conversion increment) to generate a fraction of the normalized-and-rounded floating-point result value. For an operation where the increment addition is required to be performed, tininess detection circuitry detects the after-rounding tininess status based on a still-to-be-incremented version of the normalized-and-rounded floating-point result value prior to the increment addition by the increment circuitry.