905B hexadecimal to binary

Here we will show you how to convert the hexadecimal number 905B 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 905B from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 905B by 16⁰, multiply the second to last digit in 905B by 16¹, multiply the third to last digit in 905B by 16², multiply the fourth to last digit in 905B by 16³, and so on, until all the digits are used.

B × 16⁰ = 11
5 × 16¹ = 80
0 × 16² = 0
9 × 16³ = 36864

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 + 80 + 0 + 36864 = 36955

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.

36955 ÷ 2 = 18477 with 1 remainder
18477 ÷ 2 = 9238 with 1 remainder
9238 ÷ 2 = 4619 with 0 remainder
4619 ÷ 2 = 2309 with 1 remainder
2309 ÷ 2 = 1154 with 1 remainder
1154 ÷ 2 = 577 with 0 remainder
577 ÷ 2 = 288 with 1 remainder
288 ÷ 2 = 144 with 0 remainder
144 ÷ 2 = 72 with 0 remainder
72 ÷ 2 = 36 with 0 remainder
36 ÷ 2 = 18 with 0 remainder
18 ÷ 2 = 9 with 0 remainder
9 ÷ 2 = 4 with 1 remainder
4 ÷ 2 = 2 with 0 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 905B hexadecimal to binary:

905B hexadecimal = 1001000001011011 binary

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