(a) Complete the table to compare the BCD and pure binary representations of each denary number. Denary BCD Pure binary 39 85 127 [4]
Question 1 Report
(a) Complete the table to compare the BCD and pure binary representations of each denary number.
| Denary | BCD | Pure binary |
|---|---|---|
| 39 | ||
| 85 | ||
| 127 |
[4]
Answer Details
(a) Comparing BCD and pure binary for each denary number:
Row 1: Denary 39
- BCD: 3 = 0011, 9 = 1001. BCD = 0011 1001.
- Pure binary: 39 = 32 + 4 + 2 + 1 = 00100111.
Row 2: Denary 85
- BCD: 8 = 1000, 5 = 0101. BCD = 1000 0101.
- Pure binary: 85 = 64 + 16 + 4 + 1 = 01010101.
Row 3: Denary 127
- BCD: 1 = 0001, 2 = 0010, 7 = 0111. BCD = 0001 0010 0111 (12 bits needed).
- Pure binary: 127 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = 01111111 (8 bits).
| Denary | BCD | Pure binary |
|---|---|---|
| 39 | 0011 1001 | 00100111 |
| 85 | 1000 0101 | 01010101 |
| 127 | 0001 0010 0111 | 01111111 |
Notice that for 127, BCD requires 12 bits while pure binary needs only 8, illustrating BCD's lower storage efficiency. [4]
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