A keyboard connected to a computer is used at a rate of 1 keystroke per second. The computer system polls the keyboard every 10 ms (milli seconds) to check for a keystroke and consumes 100 $\mu$s (micro seconds) for each poll. If it is determined after polling that a key has been pressed, the system consumes an additional 200 $\mu$s to process the keystroke. Let $T_1$ denote the fraction of a second spent in polling and processing a keystroke. In an alternative implementation, the system uses interrupts instead of polling. An interrupt is raised for every keystroke. It takes a total of 1 ms for servicing an interrupt and processing a keystroke. Let $T_2$ denote the fraction of a second spent in servicing the interrupt and processing a keystroke. The ratio $\frac{T_1}{T_2}$ is __________. (Rounded off to one decimal place)

To find the ratio $\frac{T_1}{T_2}$, calculate the total CPU time spent per second in both implementations:

### 1. Polling Implementation ($T_1$):

• Polling frequency: The keyboard is polled every $10\text{ ms}$, meaning there are:

  $$\text{Number of polls per second} = \frac{1\text{ s}}{10\text{ ms}} = \frac{1000\text{ ms}}{10\text{ ms}} = 100\text{ polls/s}$$

• Time spent in polling alone:

  $$100 \times 100\ \mu\text{s} = 10000\ \mu\text{s} = 10\text{ ms}$$

• Time spent processing the keystroke (1 keystroke per second):

  $$1 \times 200\ \mu\text{s} = 0.2\text{ ms}$$

• Total time spent per second ($T_1$):

  $$T_1 = 10\text{ ms} + 0.2\text{ ms} = 10.2\text{ ms} = 0.0102\text{ s}$$

### 2. Interrupt Implementation ($T_2$):

• Keystroke rate: $1\text{ keystroke per second}$, which raises $1\text{ interrupt per second}$.

• Time taken to service the interrupt and process the keystroke:

  $$T_2 = 1\text{ ms} = 0.001\text{ s}$$

### 3. Calculating the Ratio $\frac{T_1}{T_2}$:

Thus, the ratio is 10.2.