CODEWITHSUNDEEP
floating-pointieee-754
OOD Waterball
OOD Waterball

Reputation: 801

How to perform a multiplication to a floating point number represented in IEEE754

Given a floating point number M represented in IEEE754 as
0 10000000 01010101010101010101010

How to compute the result of Round(Mx20) ?

I know how to translate M into normalized form,
M = 1.01010101010101010101010(base 2) x 2^1

But I don't know how to do the multiplication M x 20 by hand effectively, because there are so many numbers in mantissa.
any hint is appreciated!

Upvotes: 1

Views: 215

Answers (1)

Eric Postpischil
Eric Postpischil

Reputation: 222273

The way forward is the standard Long Multiplication method, but in base 2:

1.010101010101010101010102•21 × 20
= 1.010101010101010101010102•21 × 5•4
= 1.010101010101010101010102•21 × 5•22
= 1.010101010101010101010102•21 × 1012•22

    1.010101010101010101010102 • 21
                          1012 • 22
× _________________________________
    1.010101010101010101010102 • 23
   00.000000000000000000000002 • 23
  101.010101010101010101010002 • 23
+ _________________________________
  110.101010101010101010100102 • 23

Then we want to round the significand to 24 bits, shown in bold: 110.101010101010101010100102 • 23.

So the result is 110.10101010101010101012 • 23, or 1.10101010101010101010100102 • 25.

Upvotes: 2

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