A programmable integrated circuit device is programmed to normalize multiplication operations by examining the input or output values to determined the likelihood of overflow or underflow and then to adjust the input or output values accordingly. The examination of the inputs can include an examination of the number of adder stages feeding into the inputs, as well as a count of leading bits ahead of the first significant bit. Adjustment of an input can include shifting the mantissa by the leading bit count and adjusting the exponent accordingly, while adjustment of the output can include shifting the mantissa by the sum of the leading bit counts of the inputs and adjusting the exponent accordingly. Or the output can be examined to find its leading bit count and the output then can be adjusted by shifting the mantissa by the leading bit count and adjusting the exponent accordingly.