8E7D hexadecimal to binary

Here we will show you how to convert the hexadecimal number 8E7D 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 8E7D from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 8E7D by 16⁰, multiply the second to last digit in 8E7D by 16¹, multiply the third to last digit in 8E7D by 16², multiply the fourth to last digit in 8E7D by 16³, and so on, until all the digits are used.

D × 16⁰ = 13
7 × 16¹ = 112
E × 16² = 3584
8 × 16³ = 32768

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:

13 + 112 + 3584 + 32768 = 36477

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.

36477 ÷ 2 = 18238 with 1 remainder
18238 ÷ 2 = 9119 with 0 remainder
9119 ÷ 2 = 4559 with 1 remainder
4559 ÷ 2 = 2279 with 1 remainder
2279 ÷ 2 = 1139 with 1 remainder
1139 ÷ 2 = 569 with 1 remainder
569 ÷ 2 = 284 with 1 remainder
284 ÷ 2 = 142 with 0 remainder
142 ÷ 2 = 71 with 0 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 8E7D hexadecimal to binary:

8E7D hexadecimal = 1000111001111101 binary

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8E7E hexadecimal to binary
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