Answer:
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.
[tex]2^{0}=1[/tex]
[tex]2^{1}=2[/tex]
[tex]2^{2}=4[/tex]
[tex]2^{3}=8[/tex]
[tex]2^{4}=16[/tex]
[tex]2^{5}=32[/tex]
[tex]2^{6}=64[/tex]
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
