IEEE Floating Point Representation | Representation of Denormalised Numbers and Special Numbers

[@ALLABOUTELECTRONICS]

Other useful videos related to Floating Point Representation: 1) IEEE 754: Single Precision and Double Precision Format: kzbin.info/www/bejne/m5Ctap-Oo7qSrNUsi=aBlp8v7sD2UY6tiQ 2) Fixed Point vs Floating Point Numbers: kzbin.info/www/bejne/sIewaYGBjdiVpaMsi=8yIaPa14s4jwg9Cw Link for the Digital Electronics (Playlist): bit.ly/31gBwMa

[@poojashah6183]

Very well explained 👌🏻👌🏻👍🏻

[@marvin5729]

Hello from Germany. Very nice explenation! I only have one question: What would the numer at minute 5:29 be in Decimal (its the -0.00011 * 2 ^-126). Could you give me a Calculation method for that pls

[@ALLABOUTELECTRONICS]

Yes, sure. First, you need to separate the given HEX number in 32 bit binary number. Then write it in a different segments. (like sign, exponent and mantissa). Here, since exponent is zero and mantissa is non-zero, it means the given number represents de-normalized number. So, it will be in the form ± 0.000 x 2 ^-126. That means here, exponent is 2^-126. Now, here since the mantissa is 00011. So, overall number will be 0. 00011 x 2^-126. More over since sign bit is 1, so number is negative number. Therefore, the equivalent decimal number is - 0.00011 x 2^-126. I hope, it will clear your doubt.

[@AlberTesla1024]

I think there is a mistake, in case of normalized numbers, the biased exponent can be between 0x01 to 0xFE, but in case of denormal number the exponent is 0, which makes the actual exponent equal to 2^-127 not 2^126. To differentiate whether the number has preceding one of not is identified by exponent value which is 1 for all normalized numbers but 0 for denormal numbers. Correct me if I am wrong.

[@ALLABOUTELECTRONICS]

The de normalized numbers are used to represent numbers which are smaller than smallest possible normalized numbers. In single precision format, the smallest positive normalized number is 1. 0 x 2^-126. So, to represent numbers between 0 and this smallest number this denorms are used. The thing of the biased exponent holds true only for normalized numbers. For denorms, the exponent is always -126. And the numbers are represented as 0. BBB x 2^-126. So, with this representation, the numbers will be less than the smallest possible normalized numbers. For example, 0.11 x 2^-126. I hope, it will clear your doubt.

[@sunandachowdhury1455]

@@ALLABOUTELECTRONICS if For denorms, the exponent is always -126, then how it represents the exponent being all 0?

[@ayan.bhunia]

Thank you 🙏👍

[@HosseinKhosravipour]

Many thanks for such an interesting explanation.

[@mayurshah9131]

You are awesome 🎉🎉

[@neelkotkar5978]

very good explanation. Thanks for helping!!! :)

[@simonepizzelli3799]

Great video!

[@rmeena6972]

awesome