AE7F hexadecimal to binary

Here we will show you how to convert the hexadecimal number AE7F 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 AE7F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in AE7F by 16⁰, multiply the second to last digit in AE7F by 16¹, multiply the third to last digit in AE7F by 16², multiply the fourth to last digit in AE7F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
7 × 16¹ = 112
E × 16² = 3584
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 + 112 + 3584 + 40960 = 44671

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.

44671 ÷ 2 = 22335 with 1 remainder
22335 ÷ 2 = 11167 with 1 remainder
11167 ÷ 2 = 5583 with 1 remainder
5583 ÷ 2 = 2791 with 1 remainder
2791 ÷ 2 = 1395 with 1 remainder
1395 ÷ 2 = 697 with 1 remainder
697 ÷ 2 = 348 with 1 remainder
348 ÷ 2 = 174 with 0 remainder
174 ÷ 2 = 87 with 0 remainder
87 ÷ 2 = 43 with 1 remainder
43 ÷ 2 = 21 with 1 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 AE7F hexadecimal to binary:

AE7F hexadecimal = 1010111001111111 binary

Hexadecimal to Binary Converter
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