BA0F hexadecimal to binary

Here we will show you how to convert the hexadecimal number BA0F 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 BA0F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in BA0F by 16⁰, multiply the second to last digit in BA0F by 16¹, multiply the third to last digit in BA0F by 16², multiply the fourth to last digit in BA0F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
0 × 16¹ = 0
A × 16² = 2560
B × 16³ = 45056

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 + 2560 + 45056 = 47631

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.

47631 ÷ 2 = 23815 with 1 remainder
23815 ÷ 2 = 11907 with 1 remainder
11907 ÷ 2 = 5953 with 1 remainder
5953 ÷ 2 = 2976 with 1 remainder
2976 ÷ 2 = 1488 with 0 remainder
1488 ÷ 2 = 744 with 0 remainder
744 ÷ 2 = 372 with 0 remainder
372 ÷ 2 = 186 with 0 remainder
186 ÷ 2 = 93 with 0 remainder
93 ÷ 2 = 46 with 1 remainder
46 ÷ 2 = 23 with 0 remainder
23 ÷ 2 = 11 with 1 remainder
11 ÷ 2 = 5 with 1 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 BA0F hexadecimal to binary:

BA0F hexadecimal = 1011101000001111 binary

Hexadecimal to Binary Converter
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