Conversion between Number Systems

We now know the four number systems used in the context of computers. The natural next step is learning to convert a number from one system to another, which is essential for understanding how numbers are represented inside a computer.

Why conversion matters — each system has its own role:

• The decimal system is the one most commonly used by humans.
• Digital systems understand only binary numbers.
• Octal and hexadecimal exist to simplify the binary representation so that we can read and manage it.

Moving between these worlds is therefore a constant necessity, and the following subsections build the complete toolkit:

• 2.3.1 — Decimal to other number systems: the repeated-division method (divide by the base, collect remainders bottom-to-top), applied to binary, octal and hexadecimal.
• 2.3.2 — Other number systems to decimal: the positional-value method (multiply each symbol by base^position and add).
• 2.3.3 — Binary to octal/hexadecimal and vice-versa: the shortcut of grouping bits — 3 at a time for octal, 4 at a time for hexadecimal — and substituting groups directly. …