Question

Как представить вещественные числа в 4-хбайтовом представлении в формате с плавающей запятой

Answer 1

4х байтовое представление - значит под порядок числа отводится 1 байт, и 3 байта под мантиссу.
И там и там первый разряд отвечает за знак.

Answer 2

Representing Real Numbers in 4-Byte Floating Point Format

Real numbers can be represented in computers using a 4-byte floating point format as specified by the IEEE 754 standard. This format uses 1 bit for the sign of the number, 8 bits for the exponent, and 23 bits for the significand (mantissa).

Some key points about the 4-byte floating point format:

- The sign bit indicates if the number is positive or negative. 0 indicates positive, 1 indicates negative.

- The exponent is stored as a biased value, with the bias being 127. So the actual exponent value is the stored value minus 127. This allows the representation of exponents in the range of -126 to 127.

- The significand is stored with an implicit leading 1. So the highest bit is always 1, even if it's not stored. This allows for a higher precision by using all 23 bits for the significand.

- Normalized numbers have a nonzero exponent. Denormalized numbers have a 0 exponent, but a nonzero significand. This allows representing numbers close to 0.

- The largest and smallest representable numbers are approximately 3.4x10^38 and 1.2x10^-38 respectively.

- Real numbers are approximated and stored in this format, so there may be small rounding errors involved. But it can represent most common real values to a reasonable precision.

So in summary, the 4-byte floating point format breaks a real number into sign, exponent and significand bits, allowing efficient representation of real values in computers based on their magnitude. It leads to a good balance between range, precision and implementation complexity.