Represent the following Decimal Numbers in 16-bit binary floating-point notation
(i)10.12510
(ii)-16.2510
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Explanation:
Have you ever wondered how computers store floating-point numbers like 3.1415 () or 9.109 × 10⁻³¹ (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)?
It seems pretty straightforward for integers (i.e. 17). Let's say we have 16 bits (2 bytes) to store the number. In 16 bits we may store the integers in a range of [0, 65535]:
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