71EF hexadecimal to binary

Here we will show you how to convert the hexadecimal number 71EF 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 71EF from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 71EF by 16⁰, multiply the second to last digit in 71EF by 16¹, multiply the third to last digit in 71EF by 16², multiply the fourth to last digit in 71EF by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
E × 16¹ = 224
1 × 16² = 256
7 × 16³ = 28672

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 + 224 + 256 + 28672 = 29167

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.

29167 ÷ 2 = 14583 with 1 remainder
14583 ÷ 2 = 7291 with 1 remainder
7291 ÷ 2 = 3645 with 1 remainder
3645 ÷ 2 = 1822 with 1 remainder
1822 ÷ 2 = 911 with 0 remainder
911 ÷ 2 = 455 with 1 remainder
455 ÷ 2 = 227 with 1 remainder
227 ÷ 2 = 113 with 1 remainder
113 ÷ 2 = 56 with 1 remainder
56 ÷ 2 = 28 with 0 remainder
28 ÷ 2 = 14 with 0 remainder
14 ÷ 2 = 7 with 0 remainder
7 ÷ 2 = 3 with 1 remainder
3 ÷ 2 = 1 with 1 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 71EF hexadecimal to binary:

71EF hexadecimal = 111000111101111 binary

Hexadecimal to Binary Converter
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