Conversion from Decimal to Binary
When converting from decimal to binary, we are essentially converting a base-10 number system (decimal) to a base-2 number system (binary). In decimal, each digit's place represents a power of 10 (e.g., 10^0, 10^1, 10^2, etc.), while in binary, each digit's place represents a power of 2 (e.g., 2^0, 2^1, 2^2, etc.). To convert a decimal number to binary, we repeatedly divide the decimal number by 2 and note the remainders until the quotient becomes 0. Reading the remainders in reverse order gives us the equivalent binary representation.
For example, if we want to convert the decimal number 13 to binary:
- Divide 13 by 2, we get a quotient of 6 and a remainder of 1.
- Divide 6 by 2, we get a quotient of 3 and a remainder of 0.
- Divide 3 by 2, we get a quotient of 1 and a remainder of 1.
- Divide 1 by 2, we get a quotient of 0 and a remainder of 1. Reading the remainders in reverse order (1101), we get the binary representation of 13. The conversion from decimal to binary is commonly used in computer science, digital electronics, and information theory for efficient data storage and manipulation.