5A8B hexadecimal to binary

Here we will show you how to convert the hexadecimal number 5A8B 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 5A8B from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 5A8B by 16⁰, multiply the second to last digit in 5A8B by 16¹, multiply the third to last digit in 5A8B by 16², multiply the fourth to last digit in 5A8B by 16³, and so on, until all the digits are used.

B × 16⁰ = 11
8 × 16¹ = 128
A × 16² = 2560
5 × 16³ = 20480

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:

11 + 128 + 2560 + 20480 = 23179

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.

23179 ÷ 2 = 11589 with 1 remainder
11589 ÷ 2 = 5794 with 1 remainder
5794 ÷ 2 = 2897 with 0 remainder
2897 ÷ 2 = 1448 with 1 remainder
1448 ÷ 2 = 724 with 0 remainder
724 ÷ 2 = 362 with 0 remainder
362 ÷ 2 = 181 with 0 remainder
181 ÷ 2 = 90 with 1 remainder
90 ÷ 2 = 45 with 0 remainder
45 ÷ 2 = 22 with 1 remainder
22 ÷ 2 = 11 with 0 remainder
11 ÷ 2 = 5 with 1 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 5A8B hexadecimal to binary:

5A8B hexadecimal = 101101010001011 binary

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