31EF hexadecimal to binary

Here we will show you how to convert the hexadecimal number 31EF 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 31EF from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 31EF by 16⁰, multiply the second to last digit in 31EF by 16¹, multiply the third to last digit in 31EF by 16², multiply the fourth to last digit in 31EF by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
E × 16¹ = 224
1 × 16² = 256
3 × 16³ = 12288

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 + 256 + 12288 = 12783

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.

12783 ÷ 2 = 6391 with 1 remainder
6391 ÷ 2 = 3195 with 1 remainder
3195 ÷ 2 = 1597 with 1 remainder
1597 ÷ 2 = 798 with 1 remainder
798 ÷ 2 = 399 with 0 remainder
399 ÷ 2 = 199 with 1 remainder
199 ÷ 2 = 99 with 1 remainder
99 ÷ 2 = 49 with 1 remainder
49 ÷ 2 = 24 with 1 remainder
24 ÷ 2 = 12 with 0 remainder
12 ÷ 2 = 6 with 0 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 31EF hexadecimal to binary:

31EF hexadecimal = 11000111101111 binary

Hexadecimal to Binary Converter
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