A7F hexadecimal to binary

Here we will show you how to convert the hexadecimal number A7F 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 A7F from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A7F by 16⁰, multiply the second to last digit in A7F by 16¹, multiply the third to last digit in A7F by 16², multiply the fourth to last digit in A7F by 16³, and so on, until all the digits are used.

F × 16⁰ = 15
7 × 16¹ = 112
A × 16² = 2560

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 + 112 + 2560 = 2687

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.

2687 ÷ 2 = 1343 with 1 remainder
1343 ÷ 2 = 671 with 1 remainder
671 ÷ 2 = 335 with 1 remainder
335 ÷ 2 = 167 with 1 remainder
167 ÷ 2 = 83 with 1 remainder
83 ÷ 2 = 41 with 1 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 A7F hexadecimal to binary:

A7F hexadecimal = 101001111111 binary

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