A31F hexadecimal to binary

Here we will show you how to convert the hexadecimal number A31F 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 A31F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A31F by 16⁰, multiply the second to last digit in A31F by 16¹, multiply the third to last digit in A31F by 16², multiply the fourth to last digit in A31F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
1 × 16¹ = 16
3 × 16² = 768
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 + 16 + 768 + 40960 = 41759

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.

41759 ÷ 2 = 20879 with 1 remainder
20879 ÷ 2 = 10439 with 1 remainder
10439 ÷ 2 = 5219 with 1 remainder
5219 ÷ 2 = 2609 with 1 remainder
2609 ÷ 2 = 1304 with 1 remainder
1304 ÷ 2 = 652 with 0 remainder
652 ÷ 2 = 326 with 0 remainder
326 ÷ 2 = 163 with 0 remainder
163 ÷ 2 = 81 with 1 remainder
81 ÷ 2 = 40 with 1 remainder
40 ÷ 2 = 20 with 0 remainder
20 ÷ 2 = 10 with 0 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 A31F hexadecimal to binary:

A31F hexadecimal = 1010001100011111 binary

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