Binary and Hexadecimal Systems: A Developer Guide to Computer Mathematics

Computers do not think in tens. Underneath the sleek user interfaces lie billions of tiny transistors that can either be ON (1) or OFF (0). Master the primary base number systems used in computer science: Binary (Base 2), Octal (Base 8), and Hexadecimal (Base 16).

Understanding Base Number Systems

In our daily life, we use Decimal (Base 10) numbers. In computer science, however, binary is the fundamental representation. To make long binary sequences human-readable, developers use Hexadecimal (Base 16) where digits range from 0 to 9, followed by letters A to F representing values 10 to 15.

How to Convert Decimal to Binary

To convert a decimal number to binary manually, repeatedly divide the number by 2 and write down the remainders in reverse order. For example, to convert 13: 13/2 = 6 (remainder 1), 6/2 = 3 (remainder 0), 3/2 = 1 (remainder 1), 1/2 = 0 (remainder 1). Reading the remainders upwards gives `1101` in binary.