Convert 2af from hexadecimal to binary. show your work.

The answer is 2AF₁₆ = 687₁₀ =  1010101111₂.

Explanation:

To convert from hexadecimal base system to binary base system, first you can do an intermediate conversion from hexadecimal to decimal using this formula:

, where position of the x₁ is the rightmost digit of the number and:

2AF₁₆ = 2*16²+A*16¹+F*16⁰ = 512 + 160 + 15 = 687₁₀

Now, transform from decimal to binary the number 687. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to 0:

Now, construct the integer part base 2 representation, by taking the remainders starting from the bottom of the list:

687₁₀ =  1010101111₂

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