Binary, Denary, and Hexadecimal Conversion Practice

This lesson provides extensive practice in converting between binary, denary, and hexadecimal — a core skill tested in OCR J277 Section 2.6. Conversion questions appear regularly in Paper 1 and often carry 2-4 marks.

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Quick Reference: Conversion Routes

    Binary <---------> Hexadecimal
      |                    |
      |   (via binary or   |
      v    direct)         v
    Denary <---------> Denary

There are six possible conversions. The most efficient routes are:

From	To	Method
Binary	Denary	Add place values where bit = 1
Denary	Binary	Place value or successive division by 2
Binary	Hex	Group into nibbles (4-bit groups)
Hex	Binary	Expand each hex digit to 4 bits
Hex	Denary	Multiply digits by powers of 16
Denary	Hex	Divide by 16, or convert via binary

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Worked Examples: Binary to Denary

Example 1: 01011010

128	64	32	16	8	4	2	1
0	1	0	1	1	0	1	0

64 + 16 + 8 + 2 = 90

Example 2: 11100001

128 + 64 + 32 + 1 = 225

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Worked Examples: Denary to Binary

Example 1: Convert 73 to binary

Using place values:

• 73 - 64 = 9 (1 in 64 column)
• 9 - 8 = 1 (1 in 8 column)
• 1 - 1 = 0 (1 in 1 column)

Result: 01001001

Check: 64 + 8 + 1 = 73. Correct!

Example 2: Convert 199 to binary

• 199 - 128 = 71
• 71 - 64 = 7
• 7 - 4 = 3
• 3 - 2 = 1
• 1 - 1 = 0

Result: 11000111

Check: 128 + 64 + 4 + 2 + 1 = 199. Correct!

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Worked Examples: Binary to Hexadecimal

Example 1: 10110100

Split: 1011 | 0100

• 1011 = B (8+2+1=11)
• 0100 = 4

Answer: B4

Example 2: 01111110

Split: 0111 | 1110

• 0111 = 7
• 1110 = E (8+4+2=14)

Answer: 7E

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Worked Examples: Hexadecimal to Binary

Example 1: Convert 9C to binary

• 9 = 1001
• C (12) = 1100

Answer: 10011100

Example 2: Convert D7 to binary

• D (13) = 1101
• 7 = 0111

Answer: 11010111

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