Algorithm for converting decimal into binary

Algorithm for Converting Decimal into Binary

1. Start by generating a sequence of powers of 2 in an array, starting from 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3), 16 (2^4), and so on.

2. Take the decimal input you want to convert into binary. For example, let's use the number 84.

3. Begin by finding the closest power of 2 that is less than or equal to the decimal input. In this case, 64 is the closest power of 2 to 84 (64 <= 84).

4. Subtract the power of 2 found in step 3 from the decimal input. In this case, 84 - 64 = 20.

5. Write down "1" in the binary representation for the power of 2 found in step 3. In our example, since 64 was used, we write "1" in the 64's place. The binary representation currently looks like this: 1______ (with a placeholder for the remaining digits).

6. Repeat steps 3-5 with the remaining difference until you reach 0. Continue to find the next closest power of 2 and update the binary representation accordingly.

7. Fill in "0" for the powers of 2 that are skipped in the process because their subtraction results are negative. For example, if the subtraction results in a negative number, fill in "0" for that power of 2 in the binary representation.

8. Once you reach 0 after subtraction, the binary representation is complete. Fill in any remaining placeholders with "0" to represent the remaining powers of 2.

9. The final binary representation of the decimal input 84 would be: 1010100.

10. Therefore, the binary representation of the decimal number 84 using the algorithm is 1010100.

By following the steps of this algorithm, you can convert any decimal number into its binary equivalent.