40FF hexadecimal to binary

Here we will show you how to convert the hexadecimal number 40FF 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 40FF from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 40FF by 16⁰, multiply the second to last digit in 40FF by 16¹, multiply the third to last digit in 40FF by 16², multiply the fourth to last digit in 40FF by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
F × 16¹ = 240
0 × 16² = 0
4 × 16³ = 16384

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 + 240 + 0 + 16384 = 16639

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.

16639 ÷ 2 = 8319 with 1 remainder
8319 ÷ 2 = 4159 with 1 remainder
4159 ÷ 2 = 2079 with 1 remainder
2079 ÷ 2 = 1039 with 1 remainder
1039 ÷ 2 = 519 with 1 remainder
519 ÷ 2 = 259 with 1 remainder
259 ÷ 2 = 129 with 1 remainder
129 ÷ 2 = 64 with 1 remainder
64 ÷ 2 = 32 with 0 remainder
32 ÷ 2 = 16 with 0 remainder
16 ÷ 2 = 8 with 0 remainder
8 ÷ 2 = 4 with 0 remainder
4 ÷ 2 = 2 with 0 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 40FF hexadecimal to binary:

40FF hexadecimal = 100000011111111 binary

Hexadecimal to Binary Converter
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