B03F hexadecimal to binary

Here we will show you how to convert the hexadecimal number B03F 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 B03F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in B03F by 16⁰, multiply the second to last digit in B03F by 16¹, multiply the third to last digit in B03F by 16², multiply the fourth to last digit in B03F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
3 × 16¹ = 48
0 × 16² = 0
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 + 48 + 0 + 45056 = 45119

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.

45119 ÷ 2 = 22559 with 1 remainder
22559 ÷ 2 = 11279 with 1 remainder
11279 ÷ 2 = 5639 with 1 remainder
5639 ÷ 2 = 2819 with 1 remainder
2819 ÷ 2 = 1409 with 1 remainder
1409 ÷ 2 = 704 with 1 remainder
704 ÷ 2 = 352 with 0 remainder
352 ÷ 2 = 176 with 0 remainder
176 ÷ 2 = 88 with 0 remainder
88 ÷ 2 = 44 with 0 remainder
44 ÷ 2 = 22 with 0 remainder
22 ÷ 2 = 11 with 0 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 B03F hexadecimal to binary:

B03F hexadecimal = 1011000000111111 binary

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