1AEF hexadecimal to binary

Here we will show you how to convert the hexadecimal number 1AEF 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 1AEF from hexadecimal to binary are explained below.

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

F × 16⁰ = 15
E × 16¹ = 224
A × 16² = 2560
1 × 16³ = 4096

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 + 224 + 2560 + 4096 = 6895

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.

6895 ÷ 2 = 3447 with 1 remainder
3447 ÷ 2 = 1723 with 1 remainder
1723 ÷ 2 = 861 with 1 remainder
861 ÷ 2 = 430 with 1 remainder
430 ÷ 2 = 215 with 0 remainder
215 ÷ 2 = 107 with 1 remainder
107 ÷ 2 = 53 with 1 remainder
53 ÷ 2 = 26 with 1 remainder
26 ÷ 2 = 13 with 0 remainder
13 ÷ 2 = 6 with 1 remainder
6 ÷ 2 = 3 with 0 remainder
3 ÷ 2 = 1 with 1 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 1AEF hexadecimal to binary:

1AEF hexadecimal = 1101011101111 binary

Hexadecimal to Binary Converter
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