1A7F hexadecimal to binary

Here we will show you how to convert the hexadecimal number 1A7F 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 1A7F from hexadecimal to binary are explained below.

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

F × 16⁰ = 15
7 × 16¹ = 112
A × 16² = 2560
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 + 112 + 2560 + 4096 = 6783

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.

6783 ÷ 2 = 3391 with 1 remainder
3391 ÷ 2 = 1695 with 1 remainder
1695 ÷ 2 = 847 with 1 remainder
847 ÷ 2 = 423 with 1 remainder
423 ÷ 2 = 211 with 1 remainder
211 ÷ 2 = 105 with 1 remainder
105 ÷ 2 = 52 with 1 remainder
52 ÷ 2 = 26 with 0 remainder
26 ÷ 2 = 13 with 0 remainder
13 ÷ 2 = 6 with 1 remainder
6 ÷ 2 = 3 with 0 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 1A7F hexadecimal to binary:

1A7F hexadecimal = 1101001111111 binary

Hexadecimal to Binary Converter
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