A08F hexadecimal to binary

Here we will show you how to convert the hexadecimal number A08F 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 A08F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A08F by 16⁰, multiply the second to last digit in A08F by 16¹, multiply the third to last digit in A08F by 16², multiply the fourth to last digit in A08F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
8 × 16¹ = 128
0 × 16² = 0
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 + 0 + 40960 = 41103

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.

41103 ÷ 2 = 20551 with 1 remainder
20551 ÷ 2 = 10275 with 1 remainder
10275 ÷ 2 = 5137 with 1 remainder
5137 ÷ 2 = 2568 with 1 remainder
2568 ÷ 2 = 1284 with 0 remainder
1284 ÷ 2 = 642 with 0 remainder
642 ÷ 2 = 321 with 0 remainder
321 ÷ 2 = 160 with 1 remainder
160 ÷ 2 = 80 with 0 remainder
80 ÷ 2 = 40 with 0 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 A08F hexadecimal to binary:

A08F hexadecimal = 1010000010001111 binary

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