8142 hexadecimal to binary

Here we will show you how to convert the hexadecimal number 8142 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 8142 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 8142 by 16⁰, multiply the second to last digit in 8142 by 16¹, multiply the third to last digit in 8142 by 16², multiply the fourth to last digit in 8142 by 16³, and so on, until all the digits are used.

2 × 16⁰ = 2
4 × 16¹ = 64
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:

2 + 64 + 256 + 32768 = 33090

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.

33090 ÷ 2 = 16545 with 0 remainder
16545 ÷ 2 = 8272 with 1 remainder
8272 ÷ 2 = 4136 with 0 remainder
4136 ÷ 2 = 2068 with 0 remainder
2068 ÷ 2 = 1034 with 0 remainder
1034 ÷ 2 = 517 with 0 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 8142 hexadecimal to binary:

8142 hexadecimal = 1000000101000010 binary

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8143 hexadecimal to binary
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