7C16 hexadecimal to binary

Here we will show you how to convert the hexadecimal number 7C16 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 7C16 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 7C16 by 16⁰, multiply the second to last digit in 7C16 by 16¹, multiply the third to last digit in 7C16 by 16², multiply the fourth to last digit in 7C16 by 16³, and so on, until all the digits are used.

6 × 16⁰ = 6
1 × 16¹ = 16
C × 16² = 3072
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:

6 + 16 + 3072 + 28672 = 31766

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.

31766 ÷ 2 = 15883 with 0 remainder
15883 ÷ 2 = 7941 with 1 remainder
7941 ÷ 2 = 3970 with 1 remainder
3970 ÷ 2 = 1985 with 0 remainder
1985 ÷ 2 = 992 with 1 remainder
992 ÷ 2 = 496 with 0 remainder
496 ÷ 2 = 248 with 0 remainder
248 ÷ 2 = 124 with 0 remainder
124 ÷ 2 = 62 with 0 remainder
62 ÷ 2 = 31 with 0 remainder
31 ÷ 2 = 15 with 1 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 7C16 hexadecimal to binary:

7C16 hexadecimal = 111110000010110 binary

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7C17 hexadecimal to binary
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