Question

Fill in the missing digits to find the base 2 representation of 59.

Answer 1

1 1 1 0 1 1

Explanation:

Answer 2

111011

Step-by-step explanation:

Following the binary rule we can find the base 2 presentation of the decimal number 59.

To find the binary equivalence of 59 we use the sum of powers of 2.

`2^(0)=1`

`2^(1)=2`

`2^(2)=4`

`2^(3)=8`

`2^(4)=16`

`2^(5)=32`

`2^(6)=64`

Now we take our number and find out what the binary number will by taking our largest number closest to the number first.

59 = 32

We chose the number 32 since 64 will be a larger value than 59.

We then check how much we have to add to 32 to get 59.

59 = 32 + 27

We then look for the closest number to 27 in our powers of 2.

59 = 32 + 16

Now we check again for how much we need left to get a total of 59.

59 = 32 + 16 + 11

Now we repeat the same process of finding which value in the powers of 2 are closest to the number.

59 = 32 + 16 + 8 + 3

59 = 32 + 16 + 8 + 2 + 1

Now since we already have a total of 59, our binary number will be all the numbers present will have a value of 1 and the numbers now used will have a number of 0.

32 16 8 4 2 1

This can also be represented as:

2^5 2^4 2^3 2^1 2^0

Now we have to include the numbers that we skipped to get the total binary number.

32 16 8 4 2 1

1 1 1 0 1 1

This can be represented as:

59 = 32 16 + 8 + 0 + 2 + 1

1 1 1 0 1 1