3E7D hexadecimal to binary

Here we will show you how to convert the hexadecimal number 3E7D 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 3E7D from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 3E7D by 16⁰, multiply the second to last digit in 3E7D by 16¹, multiply the third to last digit in 3E7D by 16², multiply the fourth to last digit in 3E7D by 16³, and so on, until all the digits are used.

D × 16⁰ = 13
7 × 16¹ = 112
E × 16² = 3584
3 × 16³ = 12288

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 + 112 + 3584 + 12288 = 15997

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.

15997 ÷ 2 = 7998 with 1 remainder
7998 ÷ 2 = 3999 with 0 remainder
3999 ÷ 2 = 1999 with 1 remainder
1999 ÷ 2 = 999 with 1 remainder
999 ÷ 2 = 499 with 1 remainder
499 ÷ 2 = 249 with 1 remainder
249 ÷ 2 = 124 with 1 remainder
124 ÷ 2 = 62 with 0 remainder
62 ÷ 2 = 31 with 0 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 3E7D hexadecimal to binary:

3E7D hexadecimal = 11111001111101 binary

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3E7E hexadecimal to binary
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