DB7C hexadecimal to binary

Here we will show you how to convert the hexadecimal number DB7C 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 DB7C from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in DB7C by 16⁰, multiply the second to last digit in DB7C by 16¹, multiply the third to last digit in DB7C by 16², multiply the fourth to last digit in DB7C by 16³, and so on, until all the digits are used.

C × 16⁰ = 12
7 × 16¹ = 112
B × 16² = 2816
D × 16³ = 53248

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 + 112 + 2816 + 53248 = 56188

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.

56188 ÷ 2 = 28094 with 0 remainder
28094 ÷ 2 = 14047 with 0 remainder
14047 ÷ 2 = 7023 with 1 remainder
7023 ÷ 2 = 3511 with 1 remainder
3511 ÷ 2 = 1755 with 1 remainder
1755 ÷ 2 = 877 with 1 remainder
877 ÷ 2 = 438 with 1 remainder
438 ÷ 2 = 219 with 0 remainder
219 ÷ 2 = 109 with 1 remainder
109 ÷ 2 = 54 with 1 remainder
54 ÷ 2 = 27 with 0 remainder
27 ÷ 2 = 13 with 1 remainder
13 ÷ 2 = 6 with 1 remainder
6 ÷ 2 = 3 with 0 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 DB7C hexadecimal to binary:

DB7C hexadecimal = 1101101101111100 binary

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