47FE hexadecimal to binary

Here we will show you how to convert the hexadecimal number 47FE 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 47FE from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 47FE by 16⁰, multiply the second to last digit in 47FE by 16¹, multiply the third to last digit in 47FE by 16², multiply the fourth to last digit in 47FE by 16³, and so on, until all the digits are used.

E × 16⁰ = 14
F × 16¹ = 240
7 × 16² = 1792
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:

14 + 240 + 1792 + 16384 = 18430

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.

18430 ÷ 2 = 9215 with 0 remainder
9215 ÷ 2 = 4607 with 1 remainder
4607 ÷ 2 = 2303 with 1 remainder
2303 ÷ 2 = 1151 with 1 remainder
1151 ÷ 2 = 575 with 1 remainder
575 ÷ 2 = 287 with 1 remainder
287 ÷ 2 = 143 with 1 remainder
143 ÷ 2 = 71 with 1 remainder
71 ÷ 2 = 35 with 1 remainder
35 ÷ 2 = 17 with 1 remainder
17 ÷ 2 = 8 with 1 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 47FE hexadecimal to binary:

47FE hexadecimal = 100011111111110 binary

Hexadecimal to Binary Converter
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47FF hexadecimal to binary
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