Question

What is the largest decimal value you can represent, using a 86-bit signed integer?

Answer 1

Answer:

$2^{85}-1$

Explanation:

Considering the number are stored using binary notations.

If there are total 86 bits and 1 bit is used as sign bit. Then in total one can have $2^{85}$ bit combinations since a bit can be either stored as 0 or as 1.

Therefore,  the largest number that can be stored will be $2^{85}-1$.

To understand it in better way let's scale down the problem to 3 bits representation. The largest number that can be stored using 3 bits is 111 which in decimal form is 7 and is equal to $2^{3}-1$.