Decimal uses digits 0–9, binary uses 0–1, octal uses 0–7, and hexadecimal uses 0–9 followed by A–F. Hexadecimal and octal are convenient compact ways to write binary values because their bases are powers of two.
Worked example
Binary 11010110 groups into 1101 and 0110. These four-bit groups are hexadecimal D and 6, so the value is D6 in hexadecimal. For octal, group from the right into 011, 010 and 110: the result is octal 326.
What to watch for
Group integer bits from the right. Leading zeros may complete a group without changing the value. A hexadecimal digit represents four bits, not four decimal digits.
Try it yourself
Convert hexadecimal 2A to binary and decimal.
Answer: 2A becomes 0010 1010 in binary. Its decimal value is 2 × 16 + 10 = 42.
How to study this topic
Write the base and bit width beside every value. Expand place weights before using a shortcut, then convert your answer back to decimal as an independent check. Representation and value are different ideas.
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