IPv4 addresses $2^{32}=4,294,967,296$

n $2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0$

Assignable IP addresses $2^h-2$

Subnets $2^s$

block size $256-Interesting Octet$

1. $2748 \div 16 = 171$ with a remainder of $12$; the hexadecimal value for $12$ is $C$.
2. $171 \div 16=10$ with a remainder of $11$; the hexadecimal value for $11$ is $B$.
3. $10 \div 16=0$ with a remainder of 10; the hexadecimal value for $10$ is $A$.
4. The decimal value $2748$ in hexadecimal format is $ABC$.

248÷2=124 124÷2=62$124÷2=62$

1: $124÷2 =62\\ 124÷2=62\\ 62÷2=31\\ 31÷2=15\\ 15÷2=7\\ 7÷2=3\\ 3÷2=1\\ 1÷2=0$

Total IPv6 $2^{128}=3.4×10^{38}$

slope-intercept form: $y=mx+b$ ;

standard quadratic form: $ax^2+bx+c=0$ ; quadratic forumal: $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

speed: $S=rt$; distance: time:

USB (Universal Serial Bus) is a standardized serial interface used to connect peripheral devices to a computer. It supports multiple device types, hot‑swapping, plug‑and‑play, and a wide range of speeds and connector formats.

USB Versions & Speeds

Your page lists the USB versions and speeds accurately, including USB 1.0 → USB4. Here is the cleaned and corrected table with modern naming:

USB Version	Marketing Name	Max Speed	Cable Length	Notes
USB 1.0 / 1.1	Low‑Speed / Full‑Speed	1.5 Mbps / 12 Mbps	3–5 m	Legacy
USB 2.0	High‑Speed	480 Mbps	5 m	Backward‑compatible with 1.1
USB 3.0 / 3.1 Gen 1	SuperSpeed 5 Gbps	5 Gbps	~3 m	Backward‑compatible with 2.0
USB 3.1 Gen 2	SuperSpeed+ 10 Gbps	10 Gbps	~3 m
USB 3.2 Gen 1×2	SuperSpeed 10 Gbps	10 Gbps	USB‑C only
USB 3.2 Gen 2×2	SuperSpeed 20 Gbps	20 Gbps	USB‑C only
USB4 (v1)	USB4 20/40 Gbps	20–40 Gbps	USB‑C only
USB4 (v2)	USB4 80/120 Gbps	80 Gbps symmetric / 120 Gbps asymmetric	USB‑C only

You should know the following facts about USB:

• USB is a serial interface that supports low- and high-speed devices. 
• USB supports almost any kind of peripheral device, including keyboards, mice, scanners, digital cameras, printers, and storage devices.
• USB supports Plug-and-Play and hot swapping (adding and removing devices without rebooting–also known as hot plugging).
• USB allows 127 devices to be connected to a single computer (directly to the host or by hubs).
• All devices connected together share computer resources (IRQs, I/O addresses).
• The computer’s BIOS must support USB and have USB enabled.

USB comes in multiple versions that perform at different rates, for various devices, as listed in the table below.

Version	Speed	Data Transfer Rate (megabits per second)	Maximum Cable Length (meters)	Supported connectors
1.0/1.1	Low-speed	1.5 Mbps	3 m	USB 3.0 Standard-A, USB 3.0 Standard-B, USB 3.0 Micro-B, USB 3.0 Micro-A, USB 3.0 Micro-AB, USB-C
	Full-speed	12 Mbps	5 m
2.0	High-speed	480 Mbps	5 m
3.1 Gen 1×1 (3.0/3.1 Gen 1)	Super-Speed	Up to 5 Gbps	3 m
3.2 Gen 2×1 (3.1 Gen 2)	SuperSpeed USB 10Gbps	Up to 10 Gbps
3.2 Gen 1×2				USB-C
3.2 Gen 2×2	SuperSpeed USB 20Gbps	Up to 20 Gbps
4		20 Gbps / 40 Gbps
4 version 2		80 Gbps Symmetrically (Up to 120 Gbps asymmetrically)

** Version 2.0 is backwards compatible with version 1.1 devices. Likewise, Version 3.0 is backwards compatible with version 2.0 devices. Most motherboards allow you to enable/disable USB support in the BIOS, or configure the USB version that will be used.

Connector	Description
USB Type‑A	Rectangular connector that generally plugs directly into the computer or a hub.
USB Type‑B	Square/D‑shaped connector used for printers, hubs, and some peripherals.
Mini‑USB (4 pin)	Small square connector designed to plug in to devices with mini plugs such as a digital camera. Most USB cables with a mini connector have an A connector on the other end to connect to the computer
Mini‑USB (5 pin)	Small connector designed to plug in to devices with mini plugs such as a digital camera.
Micro‑USB	Micro USB connectors are designed for smart phones and tablet devices. As such, micro USB connectors are quickly replacing mini USB connectors. Micro USB connectors are approximately half the thickness of Mini USB connectors, making them more appropriate for smaller devices.
USB‑C	Reversible connector supporting USB 3.x, USB4, Thunderbolt 3/4, DisplayPort Alt Mode, and power delivery.

You can connect a USB device to a computer in two ways:

• Directly to a USB port on a computer (it is common for a computer to have two USB ports). In addition, many motherboards include additional USB headers that can be used to attach additional USB ports.
• To an external USB hub. Hubs can be chained together to provide additional ports. A hub has a single B connector to connect to the computer, and multiple A connectors for attaching devices.

USB devices can be classified according to how they receive power.

Device Type	Description
Self-powered	Devices that rely on their own power supply (in other words, you plug them into an AC outlet) are self-powered devices (sometimes called active devices). All devices that draw more than 500 mA of power are required to be self-powered.
Bus powered	USB cables have wires to carry both power and data. Bus-powered (sometimes called passive) devices get their power from the USB cable. Bus-powered devices are classified as low-powered or high-powered devices depending on the amount of power they draw from the USB bus. Low powered devices use 100 mA or less High-powered devices use between 100 and 500 mA Like USB devices, USB hubs can be bus-powered or self-powered. You cannot connect high-powered devices to a bus-powered hub (you can only connect low-powered or self-powered devices to a bus-powered hub). Therefore, self-powered hubs that provide 500 mA per port are recommended to ensure an adequate power supply to all bus-powered devices that you may wish to connect to the hub.

** To install a USB device, you typically install the software driver before attaching the device. When you plug in the device, it will be automatically detected and configured.

USB Power Types

Self‑Powered Devices

Devices with their own AC power supply. Required for devices drawing more than 500 mA.

Bus‑Powered Devices

Devices powered directly from the USB port. Current page

• Low‑power: ≤100 mA
• High‑power: 100–500 mA

USB Hubs

• Can be bus‑powered or self‑powered
• High‑power devices cannot be connected to bus‑powered hubs Current page
• Self‑powered hubs recommended for reliability

USB Installation & Detection

Your page correctly states:

• Install drivers before plugging in the device
• Device is auto‑detected when connected Current page

This is still true for many legacy devices, though modern OSes often include built‑in drivers.