BCD4 hexadecimal to binary

Here we will show you how to convert the hexadecimal number BCD4 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 BCD4 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in BCD4 by 16⁰, multiply the second to last digit in BCD4 by 16¹, multiply the third to last digit in BCD4 by 16², multiply the fourth to last digit in BCD4 by 16³, and so on, until all the digits are used.

4 × 16⁰ = 4
D × 16¹ = 208
C × 16² = 3072
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:

4 + 208 + 3072 + 45056 = 48340

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.

48340 ÷ 2 = 24170 with 0 remainder
24170 ÷ 2 = 12085 with 0 remainder
12085 ÷ 2 = 6042 with 1 remainder
6042 ÷ 2 = 3021 with 0 remainder
3021 ÷ 2 = 1510 with 1 remainder
1510 ÷ 2 = 755 with 0 remainder
755 ÷ 2 = 377 with 1 remainder
377 ÷ 2 = 188 with 1 remainder
188 ÷ 2 = 94 with 0 remainder
94 ÷ 2 = 47 with 0 remainder
47 ÷ 2 = 23 with 1 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 BCD4 hexadecimal to binary:

BCD4 hexadecimal = 1011110011010100 binary

Hexadecimal to Binary Converter
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