10BC hexadecimal to binary

Here we will show you how to convert the hexadecimal number 10BC 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 10BC from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 10BC by 16⁰, multiply the second to last digit in 10BC by 16¹, multiply the third to last digit in 10BC by 16², multiply the fourth to last digit in 10BC by 16³, and so on, until all the digits are used.

C × 16⁰ = 12
B × 16¹ = 176
0 × 16² = 0
1 × 16³ = 4096

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:

12 + 176 + 0 + 4096 = 4284

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.

4284 ÷ 2 = 2142 with 0 remainder
2142 ÷ 2 = 1071 with 0 remainder
1071 ÷ 2 = 535 with 1 remainder
535 ÷ 2 = 267 with 1 remainder
267 ÷ 2 = 133 with 1 remainder
133 ÷ 2 = 66 with 1 remainder
66 ÷ 2 = 33 with 0 remainder
33 ÷ 2 = 16 with 1 remainder
16 ÷ 2 = 8 with 0 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 10BC hexadecimal to binary:

10BC hexadecimal = 1000010111100 binary

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10BD hexadecimal to binary
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