Convert among binary, octal, decimal and hexadecimal.
Decimal to binary: repeatedly divide by 2 and collect remainders. Binary to hex: group by four. Fractions: multiply by 2. BCD encodes each decimal digit in 4 bits. Know powers of two to speed conversions.
Decimal 45 = 101101₂ = 0x2D.
Hexadecimal is compact and maps neatly onto bytes, so it is the standard way to read memory dumps, colours and register values.
Convert among binary, octal, decimal and hexadecimal.
Hexadecimal is compact and maps neatly onto bytes, so it is the standard way to read memory dumps, colours and register values.
Each hex digit represents exactly four bits, so a byte is two hex digits, which makes long binary numbers short and readable.
Multiply each digit by a power of sixteen and sum the results, such as 0x1F equals 1 times 16 plus 15 for 31.
Typical applications include reading a register map in a microcontroller datasheet, writing a colour value as a six-digit hex code for a display and checking a memory dump during debugging.
Study "Binary numbers" first (topic 34 of 104 in Electronics & Embedded). It covers the groundwork this topic builds on.
0xFF = 255. Octal groups of three bits. ASCII codes characters.
Decimal 45 = 101101₂ = 0x2D.
The next topic is "Two's complement", which builds directly on this one.
It is classed as Beginner in Electronics & Embedded (topic 35 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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