BA7B hexadecimal to binary

Here we will show you how to convert the hexadecimal number BA7B 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 BA7B from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in BA7B by 16⁰, multiply the second to last digit in BA7B by 16¹, multiply the third to last digit in BA7B by 16², multiply the fourth to last digit in BA7B by 16³, and so on, until all the digits are used.

B × 16⁰ = 11
7 × 16¹ = 112
A × 16² = 2560
B × 16³ = 45056

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 + 112 + 2560 + 45056 = 47739

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.

47739 ÷ 2 = 23869 with 1 remainder
23869 ÷ 2 = 11934 with 1 remainder
11934 ÷ 2 = 5967 with 0 remainder
5967 ÷ 2 = 2983 with 1 remainder
2983 ÷ 2 = 1491 with 1 remainder
1491 ÷ 2 = 745 with 1 remainder
745 ÷ 2 = 372 with 1 remainder
372 ÷ 2 = 186 with 0 remainder
186 ÷ 2 = 93 with 0 remainder
93 ÷ 2 = 46 with 1 remainder
46 ÷ 2 = 23 with 0 remainder
23 ÷ 2 = 11 with 1 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 BA7B hexadecimal to binary:

BA7B hexadecimal = 1011101001111011 binary

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