B102 hexadecimal to binary

Here we will show you how to convert the hexadecimal number B102 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 B102 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in B102 by 16⁰, multiply the second to last digit in B102 by 16¹, multiply the third to last digit in B102 by 16², multiply the fourth to last digit in B102 by 16³, and so on, until all the digits are used.

2 × 16⁰ = 2
0 × 16¹ = 0
1 × 16² = 256
B × 16³ = 45056

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 + 0 + 256 + 45056 = 45314

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.

45314 ÷ 2 = 22657 with 0 remainder
22657 ÷ 2 = 11328 with 1 remainder
11328 ÷ 2 = 5664 with 0 remainder
5664 ÷ 2 = 2832 with 0 remainder
2832 ÷ 2 = 1416 with 0 remainder
1416 ÷ 2 = 708 with 0 remainder
708 ÷ 2 = 354 with 0 remainder
354 ÷ 2 = 177 with 0 remainder
177 ÷ 2 = 88 with 1 remainder
88 ÷ 2 = 44 with 0 remainder
44 ÷ 2 = 22 with 0 remainder
22 ÷ 2 = 11 with 0 remainder
11 ÷ 2 = 5 with 1 remainder
5 ÷ 2 = 2 with 1 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 B102 hexadecimal to binary:

B102 hexadecimal = 1011000100000010 binary

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B103 hexadecimal to binary
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