(a) Convert each binary number to denary. Show your working. [4] Binary Working Denary 10110 11001100 01010101 11111111 (b) Convert each denary number to bi...
Question 1 Report
(a) Convert each binary number to denary. Show your working. [4]
| Binary | Working | Denary |
|---|---|---|
| 10110 | ||
| 11001100 | ||
| 01010101 | ||
| 11111111 |
(b) Convert each denary number to binary. Show your working. [4]
| Denary | Working | Binary |
|---|---|---|
| 42 | ||
| 100 |
(c) State the maximum denary value that can be stored in 8 bits. Explain your answer. [2]
Answer Details
(a) Binary to denary conversions. Each binary digit represents a power of 2, with the rightmost bit being \(2^0\). [4]
| Binary | Working | Denary |
|---|---|---|
| 10110 | \(1 \times 16 + 0 \times 8 + 1 \times 4 + 1 \times 2 + 0 \times 1 = 16 + 4 + 2\) | 22 |
| 11001100 | \(128 + 64 + 0 + 0 + 8 + 4 + 0 + 0\) | 204 |
| 01010101 | \(0 + 64 + 0 + 16 + 0 + 4 + 0 + 1\) | 85 |
| 11111111 | \(128 + 64 + 32 + 16 + 8 + 4 + 2 + 1\) | 255 |
(b) Denary to binary conversions using repeated division by 2. [4]
| Denary | Division working | Binary |
|---|---|---|
| 42 | 42/2=21 r0, 21/2=10 r1, 10/2=5 r0, 5/2=2 r1, 2/2=1 r0, 1/2=0 r1. Read remainders bottom-to-top. | 101010 |
| 100 | 100/2=50 r0, 50/2=25 r0, 25/2=12 r1, 12/2=6 r0, 6/2=3 r0, 3/2=1 r1, 1/2=0 r1. Read remainders bottom-to-top. | 1100100 |
(c) The maximum denary value that can be stored in 8 bits is 255. [2]
With 8 bits, the largest number has all bits set to 1: 11111111. This equals \(2^8 - 1 = 256 - 1 = 255\). Each additional bit doubles the number of values that can be represented.
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