Question

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

Answer 1

`2^(85)-1`

Step-by-step 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`.