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This lesson provides exam-style practice for the Data Representation topic of OCR J277 Paper 1 (Computer Systems). Data representation questions are a staple of Paper 1 and test your ability to convert between number systems, calculate file sizes, and explain encoding and compression.
| Question type | Typical marks | Skills tested |
|---|---|---|
| Number system conversions | 1-3 | Binary, denary, hex conversions |
| Binary addition | 2-3 | Adding two 8-bit numbers, identifying overflow |
| Binary shifts | 2-3 | Left/right shifts, stating effect on value |
| File size calculation (image) | 3-4 | Using width x height x colour depth formula |
| File size calculation (sound) | 3-4 | Using sample rate x bit depth x duration formula |
| ASCII/Unicode comparison | 2-4 | Explaining differences, advantages, disadvantages |
| Compression explanation | 3-6 | Lossy vs lossless, RLE, Huffman coding |
| Unit conversions | 1-2 | Converting between bits, bytes, KB, MB, etc. |
Convert the binary number 11010110 to denary.
128 + 64 + 16 + 4 + 2 = 214
Convert the denary number 189 to hexadecimal.
Method: Convert to binary first.
Answer: BD
Alternative: 189 / 16 = 11 remainder 13. 11 = B, 13 = D. Answer: BD
Add the binary numbers 01110101 and 00101110. State if overflow occurs.
Carry: 1 1 1 1 1 1
0 1 1 1 0 1 0 1 (117)
+ 0 0 1 0 1 1 1 0 ( 46)
------------------
1 0 1 0 0 0 1 1 (163)
Answer: 10100011 (163). No overflow because the result fits in 8 bits.
OCR Exam Tip: Overflow occurs when a carry is generated from the most significant bit (leftmost). If both numbers start with 0 (positive) and the result starts with 1, check carefully — for unsigned integers, the result is valid as long as it fits in 8 bits.
Perform a logical left shift by 2 positions on the binary number 00010100 (20). State the new denary value.
Before: 00010100 (20) After: 01010000 (80)
The value has been multiplied by 4 (2^2). 20 x 4 = 80.
A digital photograph has a resolution of 2048 x 1536 pixels and uses 24-bit colour depth. Calculate the file size in megabytes (MB).
| Step | Calculation | Result |
|---|---|---|
| Total pixels | 2048 x 1536 | 3,145,728 |
| Total bits | 3,145,728 x 24 | 75,497,472 |
| Bytes | 75,497,472 / 8 | 9,437,184 |
| MB | 9,437,184 / (1024 x 1024) | 9.0 MB |
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