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

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