1FAF hexadecimal to binary

Here we will show you how to convert the hexadecimal number 1FAF 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 1FAF from hexadecimal to binary are explained below.

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

F × 16⁰ = 15
A × 16¹ = 160
F × 16² = 3840
1 × 16³ = 4096

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:

15 + 160 + 3840 + 4096 = 8111

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.

8111 ÷ 2 = 4055 with 1 remainder
4055 ÷ 2 = 2027 with 1 remainder
2027 ÷ 2 = 1013 with 1 remainder
1013 ÷ 2 = 506 with 1 remainder
506 ÷ 2 = 253 with 0 remainder
253 ÷ 2 = 126 with 1 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 1FAF hexadecimal to binary:

1FAF hexadecimal = 1111110101111 binary

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