817A hexadecimal to binary

Here we will show you how to convert the hexadecimal number 817A 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 817A from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 817A by 16⁰, multiply the second to last digit in 817A by 16¹, multiply the third to last digit in 817A by 16², multiply the fourth to last digit in 817A by 16³, and so on, until all the digits are used.

A × 16⁰ = 10
7 × 16¹ = 112
1 × 16² = 256
8 × 16³ = 32768

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 + 112 + 256 + 32768 = 33146

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.

33146 ÷ 2 = 16573 with 0 remainder
16573 ÷ 2 = 8286 with 1 remainder
8286 ÷ 2 = 4143 with 0 remainder
4143 ÷ 2 = 2071 with 1 remainder
2071 ÷ 2 = 1035 with 1 remainder
1035 ÷ 2 = 517 with 1 remainder
517 ÷ 2 = 258 with 1 remainder
258 ÷ 2 = 129 with 0 remainder
129 ÷ 2 = 64 with 1 remainder
64 ÷ 2 = 32 with 0 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 817A hexadecimal to binary:

817A hexadecimal = 1000000101111010 binary

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817B hexadecimal to binary
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