In a fixed-point format with a 16-bit fractional field, we have 16 bits dedicated to representing the fractional part of a number. In binary representation, each bit can have two possible values (0 or 1). Therefore, for 16 bits, we have 216 unique combinations.
216=65536
However, we need to account for the fact that in a fractional field, we are representing fractions between 0 and 1. Therefore, the maximum value we can represent with 16 bits in the fractional field is when all bits are set to 1: 1111 1111 1111 1111
In binary, this corresponds to 0.1111 1111 1111 11112 in fractional form, which is 1-2-16 in decimal form. This is slightly less than 1 because we can’t represent the value 1 itself in this format.
So, the number of unique fractional values that can be represented in a 16-bit fractional field is 2-16 -1
which is 65536 – 1 = 65535. However, we should also consider the value 0, so the total unique fractional values are 65535 + 1 = 65536.