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: IEEE 754 Standard ...  

2) Fixed Point vs Floating Point Numbers:
   • Floating Point Numbers | Fixed Point Numbe...  

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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