IEEE 754 Standard for Floating Point Binary Arithmetic

This computer science video describes the IEEE 754 standard for floating point binary. The layouts of single precision, double precision and quadruple precision floating point binary numbers are described, including the sign bit, the biased exponent and the mantissa. Examples of how to convert between denary (base 10) and single precision floating point binary numbers are shown, including how to round the mantissa correctly. There are also some example conversions that you can try yourself, along with their solutions. The way the exponent bias works and why this particular technique is used in the IEEE 754 standard, rather than two’s complement, is demonstrated. Some reserved exponent values are also mentioned.

0:00 Introduction
0:14 Review of fixed point binary
1:02 Review of floating point binary using two's complement
2:44 The IEEE 754 standard
4:08 Conversion from denary to single precision floating point binary
8:25 The exponent bias
13:42 Example conversions and solutions

[MuyenKamrannehal]

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[neolordpro]

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[NoName-tjdm]

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[LoudnessWar]

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[hayden.A]

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[bobdemp]

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[annilator]

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[segafrompk]

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[MyNameIsOlle]

4:08 is an incredibly well thought out, easy to follow, pedagogical explanation of conversion! Thanks a bunch!

[xinguangmingwo]

Your video taught me IEEE 754. Thank you.

[MIbrahimKh]

Really made me "floating" with joy, thanks teacher!

[swun]

your way of saying Mantissa is just so perfect. has to be said.

[linguae_terrae]

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[poserGirl]

this is such a good video! I never had the idea of using what you call the "modified gadget" for the place values of 2s complement numbers. I came here thinking I knew my 2s complement and I'm leaving having learned not only the standard for floating point numbers, but an incredibly valuable tool for working with 2s complement. Thank you!

[kellerw]

Thanks so much for this video, excellently paced for taking notes and really absorbing and understanding the information, with lots of great explanations as to WHY steps are taken. TY