Multiplying Floating Point Numbers

• Recall that fp is scientific notation, so arithmetic is logarithmic

  • Add the exponents (reduce by the bias), multiply the mantissas and renormalize if needed

0.75 x 24 = 0.11 x 11000

1.1x2-1 times 1.1x24

Add exponents: -1 + 4 = 3

Multiply fractions:

1.1

1.1

1 1

1 1

1 0.0 1

Result: 10.01x23 = 10010

or 1.001x24 normalized

0.75 x 24 = 0.11 x 11000

1.1x2126 times 1.1x2131

Add exponents:

126+131 = 257-127 = 130

Multiply fractions:

1.1

1.1

1 1

1 1

1 0.0 1

Result: 10.01x2130 = 1.001x2131

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