DEC2 hexadecimal to binary

Here we will show you how to convert the hexadecimal number DEC2 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 DEC2 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in DEC2 by 16⁰, multiply the second to last digit in DEC2 by 16¹, multiply the third to last digit in DEC2 by 16², multiply the fourth to last digit in DEC2 by 16³, and so on, until all the digits are used.

2 × 16⁰ = 2
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:

2 + 192 + 3584 + 53248 = 57026

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.

57026 ÷ 2 = 28513 with 0 remainder
28513 ÷ 2 = 14256 with 1 remainder
14256 ÷ 2 = 7128 with 0 remainder
7128 ÷ 2 = 3564 with 0 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 DEC2 hexadecimal to binary:

DEC2 hexadecimal = 1101111011000010 binary

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