AAAF hexadecimal to binary

Here we will show you how to convert the hexadecimal number AAAF 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 AAAF from hexadecimal to binary are explained below.

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

F × 16⁰ = 15
A × 16¹ = 160
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 + 160 + 2560 + 40960 = 43695

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.

43695 ÷ 2 = 21847 with 1 remainder
21847 ÷ 2 = 10923 with 1 remainder
10923 ÷ 2 = 5461 with 1 remainder
5461 ÷ 2 = 2730 with 1 remainder
2730 ÷ 2 = 1365 with 0 remainder
1365 ÷ 2 = 682 with 1 remainder
682 ÷ 2 = 341 with 0 remainder
341 ÷ 2 = 170 with 1 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 AAAF hexadecimal to binary:

AAAF hexadecimal = 1010101010101111 binary

Hexadecimal to Binary Converter
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