You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
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.
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 |
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
Example 1: Convert 73 to binary
Using place values:
Result: 01001001
Check: 64 + 8 + 1 = 73. Correct!
Example 2: Convert 199 to binary
Result: 11000111
Check: 128 + 64 + 4 + 2 + 1 = 199. Correct!
Example 1: 10110100
Split: 1011 | 0100
Answer: B4
Example 2: 01111110
Split: 0111 | 1110
Answer: 7E
Example 1: Convert 9C to binary
Answer: 10011100
Example 2: Convert D7 to binary
Answer: 11010111
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.