Submit HW1

hanggrian · Jun 7, 2023 · e0a8540 · e0a8540
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diff --git a/assignments/hw1.md b/assignments/hw1.md
@@ -21,7 +21,7 @@
 > We would like to send 4 bits per level of a digital signal. How many signal
   level are needed?
 
-**Using [digital signals](https://github.com/hendraanggrian/IIT-CS455/blob/main/signal.md#digital-signals)**:
+**Using [digital signals](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#digital-signals)**:
 
 $$
 \begin{array}{rcl}
@@ -31,39 +31,27 @@ $$
 \end{array}
 $$
 
-Represented as:
-
-| # | Binary | Decimal |
-| ---: | --- | --- |
-| 1 | `0000` | 0 |
-| 2 | `0001` | 1 |
-| 3 | `0010` | 2 |
-| 4 | `0011` | 3 |
-| 5 | `0100` | 4 |
-| 6 | `0101` | 5 |
-| 7 | `0110` | 6 |
-| 8 | `0111` | 7 |
-| 9 | `1000` | 8 |
-| 10 | `1001` | 9 |
-| 11 | `1010` | 10 |
-| 12 | `1011` | 11 |
-| 13 | `1100` | 12 |
-| 14 | `1101` | 13 |
-| 15 | `1110` | 14 |
-| 16 | `1111` | 15 |
+Illustrated as:
+
+| Binary | Decimal | Binary | Decimal | Binary | Decimal | Binary | Decimal |
+| ---: | :--- | ---: | :--- | ---: | :--- | ---: | :--- |
+| `0000` | 0 | `0100` | 4 | `1000` | 8 | `1100` | 12 |
+| `0001` | 1 | `0101` | 5 | `1001` | 9 | `1101` | 13 |
+| `0010` | 2 | `0110` | 6 | `1010` | 10 | `1110` | 14 |
+| `0011` | 3 | `0111` | 7 | `1011` | 11 | `1111` | 15 |
 
 ## Problem 3
 
 > A computer monitor has the resolution of $1200 \times 1000$ pixels. If each
   pixel uses $1026$ colors, how many bits are needed to send the complete
   contents of a screen?
 
-**Using [bit rate](https://github.com/hendraanggrian/IIT-CS455/blob/main/signal.md#bit-rate)**:
+**Using [bit rate](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#bit-rate)**:
 
 $$
 \begin{array}{rcl}
-  B & = & F . W . H . P \\\\
-  & = & 1,200 \times 1,000 \times \log_{2}{1,026} \\\\
+  B & = & F . R . P \\\\
+  & = & 1 \times 1,200 \times 1,000 \times \log_{2}{1,026} \\\\
   & = & \bf 12,000,000,000 \sf \ bits
 \end{array}
 $$
@@ -75,13 +63,35 @@ $$
   for the superposition of two such sine waves $f(t) = s(t) + s(t)$ and draw its
   time and frequency domain plots ($t$ denotes time).
 
+**Using [sine waves](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#sine-waves)**:
+
+$$
+\begin{array}{rcl}
+  S & = & \displaystyle A . \sin(\frac{2 \pi}P + \alpha) \\\\
+  & = & 10 \times \sin(\frac{2 \pi}{0.1} + \pi/2)
+\end{array}
+$$
+
+$$
+\begin{array}{rcl}
+  F & = & 2S \\\\
+  & = & 10 \times \sin(\frac{2 \pi}{0.1} + \pi/2) + 10 \times \sin(\frac{2 \pi}{0.1} + \pi/2) \\\\
+  & = & \bf 20 \times \sin(\frac{2 \pi}{0.1} + \pi/2)
+\end{array}
+$$
 
+Illustrated as:
+
+![](https://github.com/hendraanggrian/IIT-CS455/raw/assets/lines/hw1_analog.png)
 
 ## Problem 5
 
 > What are the disadvantages of the baseband transmission of a digital signal?
 
-
+- Limited bandwidth &mdash; Digital signals need to be approximated with analog
+  signals in case of limited bandwidth.
+- High interference &mdash; More susceptible to noises compared to modulation.
+- Short distance &mdash; Requires extra equipments to amplify.
 
 ## Problem 6
 
@@ -91,6 +101,31 @@ $$
     C = B \frac{SNR_{dB}}{3}
   $$
 
+**Using [noise](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#noise)**:
+
+$$
+\begin{array}{rcl}
+  SNR_{dB} & = & 10 . \log_{10}{SNR} \\\\
+  \frac{SNR_{dB}}{10} & = & \log_{10}{SNR}
+\end{array}
+$$
+
+**Using [Shannon capacity](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#noisy-channel-shannon-capacity)**:
+
+$$
+C = B . \log_2{(1 + SNR)}
+$$
+
+When $SNR$ is very high, we can simplify $1+SNR$.
+
+$$
+\begin{array}{rcl}
+  \log_2{SNR} & = & \log_{10}{SNR} / \log_{10}2 \\\\
+  & = & \frac{SNR_{dB}}{10} / \log_{10}2 \\\\
+  & = & SNR_{dB} / 10 . \log_{10}2 \\\\
+  & = & \bf \displaystyle \frac{SNR_{dB}}3
+\end{array}
+$$
 
 
 ## Problem 7
@@ -102,41 +137,107 @@ $$
   is amplified by $15$ dB. The power of the signal at the source $A$ is $1$ mW.
   What is the power of the signal at the destination $D$?
 
+**Using [amplification](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#amplification)** A &rarr; B:
 
+$$
+\begin{array}{rcl}
+  P_2 & = & P_1 . 10^{G / 10} \\\\
+  & = & 1 \times 10^{10 / 10} \\\\
+  & = & \bf 10 \sf \ mW
+\end{array}
+$$
+
+**Using [attenuation](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#attenuation)** B &rarr; C:
+
+$$
+\begin{array}{rcl}
+  P_3 & = & P_2 . 10^{G / 10} \\\\
+  & = & 10 \times 10^{-(0.5 \times 10) / 10} \\\\
+  & = & 10 \times 10^{-5 / 10} \\\\
+  & = & \bf 3.16 \sf \ mW
+\end{array}
+$$
+
+**Using amplification** C &rarr; D:
+
+$$
+\begin{array}{rcl}
+  P_4 & = & P_3 . 10^{G / 10} \\\\
+  & = & 3.16 \times 10^{15 / 10} \\\\
+  & = & \bf 99.92 \sf \ mW
+\end{array}
+$$
 
 ## Problem 8
 
 > Define a DC component and its effect on digital transmission.
 
+DC component is constant voltage in a signal that presents a problem in some
+scenarios:
 
+- A system that can **not** transmit low frequencies.
+- A system that uses electrical coupling via a transformer.
 
 ## Problem 9
 
 > What is the role of a header added to a data unit in the OSI network model?
 
+The roles of **network layer** in OSI model are:
 
+- Logical addressing
+- Routing
+- Internetworking
+- Packetizing
+- Fragmentation
+- Address resolution
 
 ## Problem 10
 
 > What is the difference between a logical address and a physical address?
 
-
+Logical addressing in **network layer** refers to assigned address like IP
+address. While physical addressing in **data link layer** are attached to
+hardware like MAC address.
 
 ## Problem 11
 
 > What is the total delay for a file of $2.5$ million bytes that is being sent
   over a link with a router having queuing time of $2$ microseconds and
-  processing time of $1$ microsecond. The length of the link is $1000$ km. The
-  speed of the signal is $2 \times 108$ m/s. The link has a bandwidth of $5$
+  processing time of $1$ microsecond. The length of the link is $1,000$ km. The
+  speed of the signal is $2 \times 10^8$ m/s. The link has a bandwidth of $5$
   Mbps. Which component of this delay is dominant? Which one is negligible?
 
+**Using [propagation time](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#propagation-time)**:
+
+$$
+\begin{array}{rcl}
+  PT & = & \displaystyle \frac{D}{PS} \\\\
+  & = & \frac{1,000 \textsf{ km}}{(2*10^8) \textsf{ m/s}} \\\\
+  & = & \frac{1,000,000,000 \textsf{ cm}}{200,000,000 \textsf{ m/s}} \\\\
+  & = & \bf 5 \sf \ ms
+\end{array}
+$$
+
+**Using [transmission time](https://github.com/hendraanggrian/IIT-CS455/blob/main/signals.md#transmission-time)**:
+
+$$
+\begin{array}{rcl}
+  TT & = & \displaystyle \frac{MS}{B} \\\\
+  & = & \frac{2.5 \textsf{ Mb} \times 8}{5 \textsf{ Mbps}} \\\\
+  & = & \frac{20 \textsf{ Mb}}{5 \textsf{ Mbps}} \\\\
+  & = & \bf 4 \sf \ s
+\end{array}
+$$
 
+Therefore, **propagation time is negligible**.
 
 ## Problem 12
 
 > The data input stream is `01001011`. Draw a figure presenting the output from:
 >
 > 1. AMI encoder
-> 2. differential Manchester encoder
+> 2. Differential Manchester encoder
 
+![](https://github.com/hendraanggrian/IIT-CS455/raw/assets/lines/hw1_digital.png)
 
+[View full graph](https://github.com/hendraanggrian/IIT-CS455/blob/main/lines/hw1.drawio)
diff --git a/internet.md b/internet.md
@@ -59,15 +59,15 @@ Hunders of thousands of interconnected networks.
 
 ## ISP
 
-The national Internet Service Providers (ISP) are backbone networks created and
-maintained by specialized companies. To provide connectivity between end users,
-these backbone networks are connected by complex switching stations called
-Network Access Points (NAPs).
+The national *Internet Service Providers (ISP)* are backbone networks created
+and maintained by specialized companies. To provide connectivity between end
+users, these backbone networks are connected by complex switching stations
+called *Network Access Points (NAPs)*.
 
-| Coverage | Note |
+| Coverage | Description |
 | --- | --- |
-| Regional ISP | Smaller ISPs that are connected to one or more national ISPs. |
-| Local ISP | Provide direct service to the end users. They can be connected to regional ISPs or directly to national ISPs. |
+| Regional | Smaller ISPs that are connected to one or more national ISPs. |
+| Local | Provide direct service to the end users. They can be connected to regional ISPs or directly to national ISPs. |
 
 ## Layers
 

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