In addition to the default IEEE doubleprecision format 8 byt

In addition to the default IEEE double-precision format (8 bytes, 64 bits) to store floating-point numbers, computer can also store the numbers in half-precision format (2 bytes, 16 bits). Each value is stored in 2 bytes with 1 bit for the sign, 10 bits for the mantissa, and 5 bits for the signed exponent. Determine (show your work! the smallest and largest positive floating-point numbers (in decimal value) as well as the machine epsilon for this half-precision representation. Note that the exponents range from -14 to 15.

Solution

The half-precision binary floating-point exponent is encoded using an offset-binary representation, with the zero offset being 15; also known as exponent bias in the IEEE 754 standard.

IEEE half-precision

Alternative half-precision

The smallest positive number in decimal is :- 0 00001 0000000000 = 2¹⁴ 6.10352 × 10⁵