A1CE hexadecimal to binary

Here we will show you how to convert the hexadecimal number A1CE 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 A1CE from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A1CE by 16⁰, multiply the second to last digit in A1CE by 16¹, multiply the third to last digit in A1CE by 16², multiply the fourth to last digit in A1CE by 16³, and so on, until all the digits are used.

E × 16⁰ = 14
C × 16¹ = 192
1 × 16² = 256
A × 16³ = 40960

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:

14 + 192 + 256 + 40960 = 41422

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.

41422 ÷ 2 = 20711 with 0 remainder
20711 ÷ 2 = 10355 with 1 remainder
10355 ÷ 2 = 5177 with 1 remainder
5177 ÷ 2 = 2588 with 1 remainder
2588 ÷ 2 = 1294 with 0 remainder
1294 ÷ 2 = 647 with 0 remainder
647 ÷ 2 = 323 with 1 remainder
323 ÷ 2 = 161 with 1 remainder
161 ÷ 2 = 80 with 1 remainder
80 ÷ 2 = 40 with 0 remainder
40 ÷ 2 = 20 with 0 remainder
20 ÷ 2 = 10 with 0 remainder
10 ÷ 2 = 5 with 0 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 A1CE hexadecimal to binary:

A1CE hexadecimal = 1010000111001110 binary

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A1CF hexadecimal to binary
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