The present embodiments relate to integrated circuits with floating-point arithmetic circuitry that handles normalized and denormalized floating-point numbers. The floating-point arithmetic circuitry may include a normalization circuit and a rounding circuit, and the floating-point arithmetic circuitry may generate a first result in form of a normalized, unrounded floating-point number and a second result in form of a normalized, rounded floating-point number. If desired, the floating-point arithmetic circuitry may be implemented in specialized processing blocks.