AA0F hexadecimal to binary

Here we will show you how to convert the hexadecimal number AA0F to a binary number. First note that the hexadecimal number system has sixteen different digits (0 1 2 3 4 5 6 7 8 9 A B C D E F) and the binary number system has only two different digits (0 and 1).

The four steps used to convert AA0F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in AA0F by 16⁰, multiply the second to last digit in AA0F by 16¹, multiply the third to last digit in AA0F by 16², multiply the fourth to last digit in AA0F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
0 × 16¹ = 0
A × 16² = 2560
A × 16³ = 40960

Remember that the hexadecimal number system has sixteen different digits, so when doing the above calculation, we use the following values if applicable: A=10, B=11, C=12, D=13, E=14, and F=15.

Step 2)
Next, we add up all the products we got from Step 1, like this:

15 + 0 + 2560 + 40960 = 43535

Step 3)
Now we divide the sum from Step 2 by 2. Put the remainder aside. Then divide the whole part by 2 again, and put the remainder aside again. Keep doing this until the whole part is 0.

43535 ÷ 2 = 21767 with 1 remainder
21767 ÷ 2 = 10883 with 1 remainder
10883 ÷ 2 = 5441 with 1 remainder
5441 ÷ 2 = 2720 with 1 remainder
2720 ÷ 2 = 1360 with 0 remainder
1360 ÷ 2 = 680 with 0 remainder
680 ÷ 2 = 340 with 0 remainder
340 ÷ 2 = 170 with 0 remainder
170 ÷ 2 = 85 with 0 remainder
85 ÷ 2 = 42 with 1 remainder
42 ÷ 2 = 21 with 0 remainder
21 ÷ 2 = 10 with 1 remainder
10 ÷ 2 = 5 with 0 remainder
5 ÷ 2 = 2 with 1 remainder
2 ÷ 2 = 1 with 0 remainder
1 ÷ 2 = 0 with 1 remainder

Step 4)
In the final step, we take the remainders from Step 3 and put them together in reverse order to get our answer to AA0F hexadecimal to binary:

AA0F hexadecimal = 1010101000001111 binary

Hexadecimal to Binary Converter
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