A45F hexadecimal to binary

Here we will show you how to convert the hexadecimal number A45F 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 A45F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A45F by 16⁰, multiply the second to last digit in A45F by 16¹, multiply the third to last digit in A45F by 16², multiply the fourth to last digit in A45F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
5 × 16¹ = 80
4 × 16² = 1024
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:

15 + 80 + 1024 + 40960 = 42079

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.

42079 ÷ 2 = 21039 with 1 remainder
21039 ÷ 2 = 10519 with 1 remainder
10519 ÷ 2 = 5259 with 1 remainder
5259 ÷ 2 = 2629 with 1 remainder
2629 ÷ 2 = 1314 with 1 remainder
1314 ÷ 2 = 657 with 0 remainder
657 ÷ 2 = 328 with 1 remainder
328 ÷ 2 = 164 with 0 remainder
164 ÷ 2 = 82 with 0 remainder
82 ÷ 2 = 41 with 0 remainder
41 ÷ 2 = 20 with 1 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 A45F hexadecimal to binary:

A45F hexadecimal = 1010010001011111 binary

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