Question

Jamie takes part in a quiz competition. she is asked to name the total number of combinations that the bits 1 and 0 will have in a byte. what will be her answer?

A. 256 or 28 different combinations
B. 257 or 28 different combinations
c. 255 or 28 different combinations
D. 255 or 29 different combinations

Answer 1

The answer is A

I hope this help

Answer 2

Answer: A.
`256` or
`2^8` different combinations

Step-by-step explanation:

First of all, we have two possible digits or options to choose from, bits 1 and 0. From the question, we know that every combination should form a byte. So, we have to choose eight times (eight bits). For example, a combination could be [ 10001000 ] another could be [ 00011000 ].

As you can see the order of the digits makes to change the combination. So, byte [ 10000000 ] is different than byte [ 00000001 ]. In the right math language order matter and this is called permutation. We can say that a permutation is a combinations where order matter.

For a permutation like this, where we can repeat digits, it is possible to calculate the total of permutations by using the formula,
`n` ×
`n` ×
`... (r`
`times) = n^r`

Where:

`n` is the number of digits or options to choose from

`r` is the number of digits we choose to make a permutation

From the problem we get that:

`n=2` (bits 1 and 0)

`r=8` (a permutation should form a byte)

let's replace all values into the formula :

`2` ×
`2` ×
`... (8`
`times) = 2^8 = 256`

256 permutations (combinations where order matter)

We can conclude that the total number of combinations that the bits 1 and 0 will have in a byte are A.
`256` or
`2^8` different combinations