DCEF hexadecimal to binary

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

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

F × 16⁰ = 15
E × 16¹ = 224
C × 16² = 3072
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:

15 + 224 + 3072 + 53248 = 56559

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.

56559 ÷ 2 = 28279 with 1 remainder
28279 ÷ 2 = 14139 with 1 remainder
14139 ÷ 2 = 7069 with 1 remainder
7069 ÷ 2 = 3534 with 1 remainder
3534 ÷ 2 = 1767 with 0 remainder
1767 ÷ 2 = 883 with 1 remainder
883 ÷ 2 = 441 with 1 remainder
441 ÷ 2 = 220 with 1 remainder
220 ÷ 2 = 110 with 0 remainder
110 ÷ 2 = 55 with 0 remainder
55 ÷ 2 = 27 with 1 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 DCEF hexadecimal to binary:

DCEF hexadecimal = 1101110011101111 binary

Hexadecimal to Binary Converter
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