
Here we will show you how to convert the hexadecimal number 78AE 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 78AE from hexadecimal to binary are explained below.
Step 1)
Multiply the last digit in 78AE by 16⁰, multiply the second to last digit in 78AE by 16¹, multiply the third to last digit in 78AE by 16², multiply the fourth to last digit in 78AE by 16³, and so on, until all the digits are used.
E × 16⁰ = 14
A × 16¹ = 160
8 × 16² = 2048
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:
14 + 160 + 2048 + 28672 = 30894
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.
30894 ÷ 2 = 15447 with 0 remainder
15447 ÷ 2 = 7723 with 1 remainder
7723 ÷ 2 = 3861 with 1 remainder
3861 ÷ 2 = 1930 with 1 remainder
1930 ÷ 2 = 965 with 0 remainder
965 ÷ 2 = 482 with 1 remainder
482 ÷ 2 = 241 with 0 remainder
241 ÷ 2 = 120 with 1 remainder
120 ÷ 2 = 60 with 0 remainder
60 ÷ 2 = 30 with 0 remainder
30 ÷ 2 = 15 with 0 remainder
15 ÷ 2 = 7 with 1 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 78AE hexadecimal to binary:
78AE hexadecimal = 111100010101110 binary
Hexadecimal to Binary Converter
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78AF hexadecimal to binary
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