Binary, Denary, and Hexadecimal Conversions

This lesson brings together all three number systems — binary, denary, and hexadecimal — and provides a comprehensive guide to converting between them. Fluency in these conversions is essential for the GCSE Computer Science exam.

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Conversion Summary Table

From	To	Method
Binary → Denary	Add up the place values of all 1-bits	Use the column headings: 128, 64, 32, 16, 8, 4, 2, 1
Denary → Binary	Subtract place values or divide by 2	Use place value method or successive division
Binary → Hex	Split into nibbles (4-bit groups)	Convert each nibble to its hex digit
Hex → Binary	Replace each hex digit with 4 bits	Use the hex-to-binary lookup table
Hex → Denary	Multiply digits by powers of 16	First digit × 16 + second digit × 1
Denary → Hex	Divide by 16	Quotient = first digit, remainder = second digit

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Worked Examples: Full Conversion Practice

Example 1: Convert denary 156 to binary and hex