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

This video explains how the IEEE 754 format represents special values like 0, infinity, NaN, and denormalized numbers in a single precision format.
Here's a detailed breakdown of what you'll learn:
In IEEE single precision format, for normalized numbers, the exponent ranges from -126 to +127. The exponent value of all 0's and all 1's is reserved for special cases.
Special Cases:
1) Zero (0): Identified by an all-zero exponent and an all-zero mantissa, representing both positive and negative zero (+0 and -0).
2) Denormalized Numbers: Represented by an all-zero exponent and a non-zero mantissa. These numbers are extremely small, even smaller than the smallest representable normalized number.
3) Infinity (±∞): Identified by an all-one exponent and a zero mantissa. The sign bit determines positive or negative infinity.
4) NaN (Not a Number): Represented by an all-one exponent and a non-zero mantissa. This special value indicates an undefined or unrepresentable result. Certain arithmetic operations can generate NaN values, such as 0/0, +∞/+∞, 0×∞, and +∞-∞.
Other useful videos related to Floating Point Representation:
1) IEEE 754: Single Precision and Double Precision Format:
• Floating Point Numbers...
2) Fixed Point vs Floating Point Numbers:
• Floating Point Numbers...
Link for the Digital Electronics (Playlist):
• Digital Electronics
This video will be helpful to all the students of science and engineering in understanding how special numbers like 0, infinity, NaN, and Denormalised Numbers are represented in IEEE 754 standard.
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[@ALLABOUTELECTRONICS]

Other useful videos related to Floating Point Representation:
1) IEEE 754: Single Precision and Double Precision Format:
ruclips.net/video/e_J9lXnU_vs/видео.htmlsi=aBlp8v7sD2UY6tiQ
2) Fixed Point vs Floating Point Numbers:
ruclips.net/video/zVM8NKXsboA/видео.htmlsi=8yIaPa14s4jwg9Cw
Link for the Digital Electronics (Playlist):
bit.ly/31gBwMa

[@poojashah6183]

Very well explained 👌🏻👌🏻👍🏻

[@ayan.bhunia]

Thank you 🙏👍

[@mayurshah9131]

You are awesome 🎉🎉

[@neelkotkar5978]

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

[@simonepizzelli3799]

Great video!

[@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.

[@rmeena6972]

awesome

[@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.