Computer Science Fundamentals Lecture Notes PDF

# Computer Science Fundamentals ## Number Systems ### Converting Numbers * **Convert (941D3)₁₆ into binary and decimal** * (1001 0100 0001 1101)₂ (Binary) * = 9 x 16³ + 4 x 16² + 13 x 16¹ + 3 x 16⁰ = 372707 (decimal) * **Co...

# Computer Science Fundamentals ## Number Systems ### Converting Numbers * **Convert (941D3)₁₆ into binary and decimal** * (1001 0100 0001 1101)₂ (Binary) * = 9 x 16³ + 4 x 16² + 13 x 16¹ + 3 x 16⁰ = 372707 (decimal) * **Convert (11011111 11010101)₂ = (12.0... )₈** * The fraction is converted by adding zeros to the right, and the integer part is converted by adding zeros to the left. * 1101 1101. 1101 0101 = 13 113. 113 5 * **Convert (2B6)₁₆** * Binary: 0010 1011 0110 ### Combining Bits * Combine 001010110110 into 3 bit * 001 010 110 = 1 2 6 * **Convert (0.513)₁₀ to octal** * 0.513 x 8 = 4.104 * 0.104 x 8 = 0.832 * 0.832 x 8 = 6.656 * 0.656 x 8 = 5.248 * 0.248 x 8 = 1.984 * 0.984 x 8 = 7.872 * So (0.513)₁₀ = (0.4065113i...)₈ * This is done by taking the integer part of the result of multiplying the fraction by 8 and adding it to the right of the decimal point. The remaining fraction is then multiplied by 8 again, and the process is repeated until the desired accuracy is achieved. ### Decimal to Octal Conversion * To convert a decimal number to an octal number, the number is repeatedly divided by 8, and the remainder is added to the right of the octal number. * For example: * Convert (0.0110)₂ to decimal. * 0 x 2^-1 + 1x2^-2 + 1 x 2^-3 + 0 x 2^-4 = 0.375 ## Computer Networks * A **computer network** is a collection of computing devices that are connected in various ways to communicate and share information and resources. * **Classifications of Networks** * **Local Area Network (LAN)**: A network that covers a small geographical area, such as a building or a campus. * **Wide Area Network (WAN)**: A network that covers a large geographical area, such as a country or continent. * **Metropolitan Area Network (MAN)**: A network that covers a metropolitan area. ## Internet * What’s the difference between Internet and World Wide Web? ## Server Client Network * **"Server, Client"** * A Server has resources(Software) and sends it to the connected devices (Clients) through **packets**. * The packets connection between the servers and clients can be via **wires** or **wireless** ## Network Topology * **Topology** is the way devices in a network are connected. * **Bus Topology:** All devices are connected to a single cable. This is a very simple topology, but it is not very reliable. * **Star Topology:** All devices are connected to a central hub. This is a more reliable topology than bus topology, but it can be more expensive. * **Mesh Topology:** All devices are connected to each other. This is the most reliable topology, but it is also the most expensive. ## Logic Gates * **Logic gates** are electronic circuits that perform logical operations. * **Buffer** output is the same as the input, but it can drive a heavier load. ### Types of Logic Gates * **Inverter:** Inverts the input signal. * **AND Gate:** Outputs 1 only when both inputs are 1. * **NAND Gate:** Outputs 0 only when both inputs are 1. * **NOR Gate:** Outputs 0 only when both inputs are 0. * **XOR Gate:** Outputs 1 when inputs are different. * **XNOR Gate:** Outputs 1 when inputs are the same. ## Timing Diagram and XOR Gate * **Timing Diagram:** A timing diagram shows the relationship between the inputs and outputs of logic gates over time. * **XOR Gate Diagram:** <start_of_image> CIRCUIT DIAGRAM | X | Y | Z | Timing Diagram |---|---|---|--- | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | Timing Diagram | 1 | 1 | 0 | * **XNOR Gate Diagram:** CIRCUIT DIAGRAM | X | Y | Z | Timing Diagram |---|---|---|--- | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | Timing Diagram | 1 | 1 | 1 | * Timing Diagram of XNOR and XOR Gate | X | Y | XNOR | XOR | |---|---|---|---| | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 1 | 0 | 0 | 1 | | 1 | 1 | 1 | 0 | Note: The "XOR" gate outputs a true value (1) when the inputs are different and a false value (0) when the inputs are the same. The "XNOR" gate is the opposite of the "XOR" gate.