Floating-Point Multiplication Algorithm

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The following figure shows the algorithm for binary floating-point multiplication, which is similar to the addition one:

Step 1. Calculating the exponent of the product

Step 2. Multiplying the significands

Step 3. Normalizing the product

Step 4. Rounding the significand

Step 5. Checking for overflow or underflow

Three comments are about the above algorithm:

• The exponent of the product is created by adding the biased exponents, being sure to subtract one bias to get the proper result.


• Set the sign bit of the product to 1 if the signs of the operands were different or to 0 if they were the same.


• The size of the exponent is used to check for overflow or underflow.