What's the biggest fixed point number that can be expressed in 8 bits?

Question

Suppose an 8-bit fixed point number x, where 7 bits are allocated to the fractional part and 1 bit to the integer part. How can I calculate the biggest possible number that can be expressed using this Q8.1 configuration? Is there a proper method to perform these calculations?

Answer 1

The largest fixed-point number will always have the same binary value as the largest integer value. If your fixed-point number is unsigned then its largest binary value is 11111111 (decimal 255). The equivalent decimal fixed-point value is just this decimal integer value divided by 2^7, or 1.9921875