Question

Double precision on this computer will use 24-bits, where 8-bits are used to store the characteristic. What is the smallest positive floating point (real) number that can be represented using double precision on this computer?

Answer 1

The smallest positive floating-point number that can be represented using double precision on this computer is 0.5 x 2^(-127).

Step-by-step explanation:

In double precision, a floating-point representation on this computer uses 24 bits, where 8 bits are used to store the characteristic. The characteristic represents the exponent of the number. Since 8 bits can represent values from 0 to 255, and we need to store both positive and negative exponents, the range of the characteristic is from -127 to 128. The smallest positive floating-point number that can be represented is when the characteristic is its lowest value of -127 and the mantissa (fractional part) is its smallest value of 0.5.

So the smallest positive floating-point number in double precision on this computer is:

0.5 x 2^(-127)