Data Representation · 4 question types
Past paper frequency (2018 to 2024)
This topic accounts for approximately 12% of your exam marks.
Binary/hex conversion and binary arithmetic appear in every Paper 1. Consistently 8 to 15 marks.
Binary addition is done column by column from right to left, just like denary addition, but with only two digits and a carry rule.
| Sum | Result | Carry |
|---|---|---|
| 0 + 0 | 0 | none |
| 0 + 1 | 1 | none |
| 1 + 0 | 1 | none |
| 1 + 1 | 0 | carry 1 (because 1 + 1 = 10 in binary) |
| 1 + 1 + 1 | 1 | carry 1 (because 1 + 1 + 1 = 11 in binary) |
The fifth rule covers the case where two 1s and an incoming carry meet in the same column.
Example — Add the 4-bit binary values 1001 and 0100.
Working from right to left:
| Column | Place value | Operation | Result bit | Carry out |
|---|---|---|---|---|
| Rightmost | 1 | 1 + 0 | 1 | 0 |
| 2nd | 2 | 0 + 0 | 0 | 0 |
| 3rd | 4 | 0 + 1 | 1 | 0 |
| 4th | 8 | 1 + 0 | 1 | 0 |
Result: 1101 (which is 13 in denary). Sanity check: 9 + 4 = 13. ✓
Example — Add the 8-bit binary values 00011001 and 10001001.
0 0 0 1 1 0 0 1 (25)
+ 1 0 0 0 1 0 0 1 (137)
-----------------
1 0 1 0 0 0 1 0 (162)
Working through column by column, applying the rules, gives 10100010 (162). Sanity check: 25 + 137 = 162. ✓