7E1D hexadecimal to binary

Here we will show you how to convert the hexadecimal number 7E1D 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 7E1D from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 7E1D by 16⁰, multiply the second to last digit in 7E1D by 16¹, multiply the third to last digit in 7E1D by 16², multiply the fourth to last digit in 7E1D by 16³, and so on, until all the digits are used.

D × 16⁰ = 13
1 × 16¹ = 16
E × 16² = 3584
7 × 16³ = 28672

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:

13 + 16 + 3584 + 28672 = 32285

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.

32285 ÷ 2 = 16142 with 1 remainder
16142 ÷ 2 = 8071 with 0 remainder
8071 ÷ 2 = 4035 with 1 remainder
4035 ÷ 2 = 2017 with 1 remainder
2017 ÷ 2 = 1008 with 1 remainder
1008 ÷ 2 = 504 with 0 remainder
504 ÷ 2 = 252 with 0 remainder
252 ÷ 2 = 126 with 0 remainder
126 ÷ 2 = 63 with 0 remainder
63 ÷ 2 = 31 with 1 remainder
31 ÷ 2 = 15 with 1 remainder
15 ÷ 2 = 7 with 1 remainder
7 ÷ 2 = 3 with 1 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 7E1D hexadecimal to binary:

7E1D hexadecimal = 111111000011101 binary

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7E1E hexadecimal to binary
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