413A hexadecimal to binary

Here we will show you how to convert the hexadecimal number 413A 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 413A from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 413A by 16⁰, multiply the second to last digit in 413A by 16¹, multiply the third to last digit in 413A by 16², multiply the fourth to last digit in 413A by 16³, and so on, until all the digits are used.

A × 16⁰ = 10
3 × 16¹ = 48
1 × 16² = 256
4 × 16³ = 16384

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:

10 + 48 + 256 + 16384 = 16698

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.

16698 ÷ 2 = 8349 with 0 remainder
8349 ÷ 2 = 4174 with 1 remainder
4174 ÷ 2 = 2087 with 0 remainder
2087 ÷ 2 = 1043 with 1 remainder
1043 ÷ 2 = 521 with 1 remainder
521 ÷ 2 = 260 with 1 remainder
260 ÷ 2 = 130 with 0 remainder
130 ÷ 2 = 65 with 0 remainder
65 ÷ 2 = 32 with 1 remainder
32 ÷ 2 = 16 with 0 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 413A hexadecimal to binary:

413A hexadecimal = 100000100111010 binary

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413B hexadecimal to binary
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