7AE2 hexadecimal to binary

Here we will show you how to convert the hexadecimal number 7AE2 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 7AE2 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 7AE2 by 16⁰, multiply the second to last digit in 7AE2 by 16¹, multiply the third to last digit in 7AE2 by 16², multiply the fourth to last digit in 7AE2 by 16³, and so on, until all the digits are used.

2 × 16⁰ = 2
E × 16¹ = 224
A × 16² = 2560
7 × 16³ = 28672

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:

2 + 224 + 2560 + 28672 = 31458

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.

31458 ÷ 2 = 15729 with 0 remainder
15729 ÷ 2 = 7864 with 1 remainder
7864 ÷ 2 = 3932 with 0 remainder
3932 ÷ 2 = 1966 with 0 remainder
1966 ÷ 2 = 983 with 0 remainder
983 ÷ 2 = 491 with 1 remainder
491 ÷ 2 = 245 with 1 remainder
245 ÷ 2 = 122 with 1 remainder
122 ÷ 2 = 61 with 0 remainder
61 ÷ 2 = 30 with 1 remainder
30 ÷ 2 = 15 with 0 remainder
15 ÷ 2 = 7 with 1 remainder
7 ÷ 2 = 3 with 1 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 7AE2 hexadecimal to binary:

7AE2 hexadecimal = 111101011100010 binary

Hexadecimal to Binary Converter
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