Calculating the total number of possibilities in binary format?

Question

How would you calculate the total number of possibilities a binary can have in one byte?

00000000through 11111111=num_of_possibilities

Answer 1

The total number is 2 for the number of bits. Thus, eight bits have 2 ⁸ possible values.

If you really mean “how to calculate it,” consider that each bit has two possible values.

So, one bit means 2 values.

Two bits have one set of two values ​​of each possible value of the other bit, therefore

00
01
10
11

which means a total value of 4 (= 2 x 2).

, 8 (= 4 ; 2) . , 8 ; 2; , 16 & times; 2 ..

, - 2 2 , 2 2 , 2 2 , 2 2 , 2 256.

Answer 2

: 2 ⁿ n - .

, 1 , 8 , 2 ⁸ 256.

Answer 3

:

• 2 ^ n, n - (2 ^ 8). .
• 1 + 1 (255 + 1) 0 () + .
• , . - , n + 1 . (2 (1 + 8 + 28 + 56) + 70) - , 0 n.