A90F hexadecimal to binary

Here we will show you how to convert the hexadecimal number A90F 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 A90F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A90F by 16⁰, multiply the second to last digit in A90F by 16¹, multiply the third to last digit in A90F by 16², multiply the fourth to last digit in A90F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
0 × 16¹ = 0
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 + 0 + 2304 + 40960 = 43279

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.

43279 ÷ 2 = 21639 with 1 remainder
21639 ÷ 2 = 10819 with 1 remainder
10819 ÷ 2 = 5409 with 1 remainder
5409 ÷ 2 = 2704 with 1 remainder
2704 ÷ 2 = 1352 with 0 remainder
1352 ÷ 2 = 676 with 0 remainder
676 ÷ 2 = 338 with 0 remainder
338 ÷ 2 = 169 with 0 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 A90F hexadecimal to binary:

A90F hexadecimal = 1010100100001111 binary

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