What is the process of converting a decimal number to binary?
To convert a decimal number to binary, each decimal digit is replaced by its binary equivalent. In a binary system, each digit represents a power of 2 (2^0, 2^1, 2^2, etc.). The binary number is then formed by combining these powers of 2 based on the given decimal number. For example, converting the decimal number 14 to binary involves representing 14 as a sum of powers of 2.
Converting Decimal to Binary:
Step 1: Write down the decimal number.
Step 2: Determine the highest power of 2 that is less than or equal to the decimal number. This will be the leftmost bit in the binary representation.
Step 3: Subtract the value of this power of 2 from the decimal number and repeat the process for the remaining value.
Step 4: Continue this process until the decimal number becomes 0, and the binary equivalent is formed by combining the powers of 2 corresponding to the bits.
Using the example of converting decimal 14 to binary:
- 14 - 8 = 6 (2^3 = 8)
- 6 - 4 = 2 (2^2 = 4)
- 2 - 2 = 0 (2^1 = 2)
Therefore, the binary representation of decimal 14 is 1110.
This process of converting decimal to binary is essential in understanding how computers represent and process data. It allows us to comprehend the binary nature of computing systems and how information is manipulated at the fundamental level.