DECF hexadecimal to binary

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

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

F × 16⁰ = 15
C × 16¹ = 192
E × 16² = 3584
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 + 192 + 3584 + 53248 = 57039

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.

57039 ÷ 2 = 28519 with 1 remainder
28519 ÷ 2 = 14259 with 1 remainder
14259 ÷ 2 = 7129 with 1 remainder
7129 ÷ 2 = 3564 with 1 remainder
3564 ÷ 2 = 1782 with 0 remainder
1782 ÷ 2 = 891 with 0 remainder
891 ÷ 2 = 445 with 1 remainder
445 ÷ 2 = 222 with 1 remainder
222 ÷ 2 = 111 with 0 remainder
111 ÷ 2 = 55 with 1 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 DECF hexadecimal to binary:

DECF hexadecimal = 1101111011001111 binary

Hexadecimal to Binary Converter
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