Question

Which 5 numbers can make any number between 1 and 31?

Answer 1

Answer: 1,2,4,8,16

Step-by-step explanation:

For any numbers between 1 and (2^n -1), they can be expressed as the sum of powers of 2 from 2^0 until 2^(n-1)

This is how the binary system works.

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Answer 2

Answer:

Any number between 1 to 31 can be represented by 1,2,4,8,16.

Step-by-step explanation:

• With the concept of binary numbers, we can easily understand the answer to the given question .

• For any numbers between 1 and $2^{n}$ - 1, the number can be expressed as the sum of powers of 2 from $2^{0}$ until $2^{(n-1)}$.

• 1 can be written as $2^{0}$ and 31 can be written as $2^{5}$ - 1 .

• So , 1 to 31  numbers can be represented using 5 bits .

1st bit will represent number $2^{0}$ = 1

2nd bit will represent number $2^{1}$  = 2

3rd bit will represent number  $2^{2}$ = 4

4th bit will represent number $2^{3}$ = 8

5th bit will represent number $2^{4}$  = 16

• Any number between 1 to 31 can be represented by 1,2,4,8,16.

        For example : 23 can be written as 16+4+2+1=23

                                30 = 16+8+4+2

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