A98F hexadecimal to binary

Here we will show you how to convert the hexadecimal number A98F 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 A98F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A98F by 16⁰, multiply the second to last digit in A98F by 16¹, multiply the third to last digit in A98F by 16², multiply the fourth to last digit in A98F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
8 × 16¹ = 128
9 × 16² = 2304
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 + 128 + 2304 + 40960 = 43407

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.

43407 ÷ 2 = 21703 with 1 remainder
21703 ÷ 2 = 10851 with 1 remainder
10851 ÷ 2 = 5425 with 1 remainder
5425 ÷ 2 = 2712 with 1 remainder
2712 ÷ 2 = 1356 with 0 remainder
1356 ÷ 2 = 678 with 0 remainder
678 ÷ 2 = 339 with 0 remainder
339 ÷ 2 = 169 with 1 remainder
169 ÷ 2 = 84 with 1 remainder
84 ÷ 2 = 42 with 0 remainder
42 ÷ 2 = 21 with 0 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 A98F hexadecimal to binary:

A98F hexadecimal = 1010100110001111 binary

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