(i) f=1 i=1 f = f * i i = i+1
f = 1 x 1 = 1 i = 2
(ii) f = 1 x 2 i = 3 = 2
(iii) f = 2 × 3 i = 4 = 6
(iv) f = 6 x 4 i = 5 (loop terminates) = 24

power (5,2) = 5 × 5  = 25
power (x, n) raise x to the power n
Algorithm :
power (x, n) 
If n = 0 -- base case
1
else -- rrecursion step
if n is odd
x * power (x, n - 1)
else 
p = power (x, n/2)
p * p
To find a ¹⁰ :

S.No Versions Logo Year Prominent feature 1. Windows 1.x 1985 1. Introduction of GUI in 16 - bit. processor
2. Mouse was introduced as an input device 2. Windows 2.x 1987 1. Supports to minimize or maximize windows.
2. Control panel feature was introduced with
various system settings and customizing options. 3. Windows 3.x 1992 1. Introduced the concept of multitasking.
2. Supported 256 colors which brought a more
modern, colorful look to the interface. 4. Windows 95 1995 1. Introduced Start button, the taskbar, Windows Explorer and Start menu.
2. Introduced 32 - bit processor and focused more on multitasking. 5. Windows 98 1998 1. Integration of the Web browser (Internet Explorer) with the Operating System.
2. DOS gaming began to disappear as Windows-based games improved.
3. Plug and play feature was introduced. 6. Windows NT   Designed to act as servers in network. 7. Windows Me 2000 It introduced automated system diagnostics and recovery tools. 8. Windows 2000 2000 1. Served as an Operating System for business
desktop and laptop systems.
2. Four versions of Windows 2000 were released: Professional (for business)
3. desktop and laptop systems), Server (both a
Web server and an office server),
4. Advanced Server (for line-of-business 
applications) and Data Centre Server (for high traffic computer networks). 9. Windows XP 2001 1. Introduced 64-bit Processor.
2. Improved Windows appearance with themes and offered a stable version 10. Windows Vista 2006 Updated the look and feel of Windows 11. Windows 7 2009 Booting time was improved, introduced new user interfaces like Aero Peek, pinning programs to the taskbar, handwriting recognition etc, and Internet Explorer 8. 12. Windows 8 2012 1. Windows 8 was faster than previous versions of Windows.
2. Start button was removed
3. Windows 8 takes better advantage of multicore processing, solid-state drives (SSD), touch screens, and other alternate input methods.
4. Served as a common platform for mobile and computer. 13. Windows 10 2015 1. Start Button was added again.
2. Multiple desktops.
3. Central Notification Center for App notification and quick actions.
4. Cortana voice-activated personal assistant.

1101011₂ - 111010₂
1101011
+111010
_______
0110001
_______
1101011₂ - 111010₂  = 0110001₂

Let the variables a, b, c represent the glass A, glass B and Glass C respectively. Variables A, B, C can store values APPLE, GRAPE or EMPTY.
Initial State:
1.-- a, b, c : = APPLE, GRAPE, EMPTY
2. C : = b
3.-- a, b, c : = APPLE, EMPTY, GRAPE
4. b : = a
5.-- a, b, c : = EMPTY, APPLE, GRAPE
6. a : = C
7.-- a, b, c : = GRAPE, APPLE, EMPTY
Final State:
Specification:
1. Exchange ()
2. -- inputs: a, b, c :- APPLE, GRAPE, EMPTY
3.--outputs: a, b, c:- GRAPE, APPLE, EMPTY

Computers size was drastically reduced. S.No	Generation	Period	Main Component used	Merits/ Demerits
1	First Generation	1942-1955		Big in size Consumed more power Malfunction due to overheating Machine Language was used Eg : ENIAC, EDVAC, UNIVAC
First Generation Computer - ENIAC, EDVAC, UNIVAC 1 ENIAC weighed about 27 tons, size 8 feet x 100 feet x 3 feet, and consumed around 150 watts of power
2	Second Generation	1955-1964		Smaller compared to First Generation Generated Less Heat Consumed less power compared to first-generation Punched cards were used. The first operating system was developed Batch Processing and Multiprogramming Operating System Machine language, as well as Assembly language, was used.
Second Generation Computers IBM 1404, IBM 1620, UNIVAC 1108
3	Third Generation	1964-1975		Computers were smaller, faster, and more reliable Consumed less power. High-Level Languages were used.
Third Generation Computers -IBM ·360 series, Honeywell 6000 series
4	Fourth Generation	1975-1980		Smaller and Faster Microcomputer series such as IBM and APPLE was developed Portable Computers were introduced.
5	Fifth Generation	1980-till date		Parallel, Processing Superconductors Computers size was drastically reduced. Can recognize Images and Graphics Introduction of Artificial Intelligence and Expert Systems Able to solve highly complex problems including decision making and logical reasoning.
6	Sixth Generation	In future		Parallel and Distributed computing Computers have become smarter faster and smaller Development of robotics Natural Language Processing Development of Voice Recognition Software.

Read-only memory (ROM):
1. Read only memory refers to special memory in a computer with pre-recorded data at manufacturing time which cannot be modified.
2. The stored programs that start the computer and perform diagnostics are available in ROMs. ROM stores critical programs such as the program that boots the computer.
3. Once the data has been written onto a ROM chip, it cannot be modified or removed and can only be read.
4. ROM retains its contents even when the computer is. turned off. So, ROM is called as a non-volatile memory.
Programmable Read-Only Memory (PROM):
1. Programmable read-only memory is also a nonvolatile memory on which data can be written only once. Once a program has been written onto a PROM, it remains there forever.
2. Unlike the main memory, PROMs retain their contents even when the computer is turned off.
3. The PROM differs from ROM. PROM is manufactured as a blank memory, whereas a ROM is programmed during the manufacturing process itself.
4. PROM programmer or a PROM burner is used to write data to a PROM chip. The process of programming a PROM is called burning the PROM.
Erasable Programmable Read-Only Memory (EPROM):
1. Erasable Programmable Read Only Memory is a special type of memory which serves as a PROM, but the content can be erased using ultraviolet rays.
2. EPROM retains its contents until it is exposed to ultraviolet light. The ultraviolet light clears its contents, making it possible to reprogram the memory.
3. An EPROM differs from a PROM, PROM can be written only once and cannot be erased.
4. EPROMs are used widely in personal computers because they enable the manufacturer to change the contents of the PROM to replace with updated versions or erase the contents before the computer is delivered.
Electrically Erasable Programmable Read Only Memory (EEPROM)
1. Electrically Erasable Programmable Read Only Memory is a special type of PROM that can be erased by exposing it to an electrical charge.
2. Like other types of PROM, EEPROM retains its contents even when the power is turned off.
3. Comparing with all other types of ROM, EEPROM is slower in performance.

98.46₁₀

2. Fractional part
0.46 x 2 = 0.92 = 0
0.92 x 2 = 1.84 = 1
0.84 x 2 = 1.68 = 1
0.68 x 2 = 1.36 = 1
0.36 x 2 = 0.72 = 0
0.72 x 2 = 1.44 = 1
98.46₁₀ = (1100010.011101...)₂

The main purpose of using an operating system:
(i) It controls and coordinates all the activities of a computer system.
(ii) It provides an environment for a computer user to execute programs on computer hardware in a convenient and efficient manner.
(iii) It enables the user to design the application, and also it provides an interface to interact with the computer and controls the execution of all kinds .of programs without knowing the internals of the hardware.
(iv) It interprets the command and instructions to perform the specified tasks.
(v) It coordinates and assigns the compilers, assemblers, utility programs to the users.
(vi) It detects errors present in the hardware and software.
(vii) It maintains the internal time clock.
(viii) It protects itself from being destroyed by any users.
(ix) It serves two major functions
1. Supervision (Prevent errors)
2. Management (Operation and control of I/O devices)
(x) It loads the program itself into memory so that user can interact with hardware and software.

1. The Central Processing Unit(CPU) has a Memory Data Register (MDR) and a Memory Address Register (MAR).
2. The Memory Data Register (MDR) keeps the data which is transferred between the Memory and the CPU. The Program Counter (PC) is a special register in the CPU which always keeps the address of the next instruction to be executed.
3. The Arithmetic and Logic unit of CPU places the address of the memory to be fetched, into the Memory Address Register.
4. A bus is a collection of wires used for communication between the internal components of a computer.
5. The address bus is used to point a memory location. A decoder, a digital circuit is used to point to the specific memory location where the word can be located.
6. The address register is connected with the address bus, which provides the address of the instruction. A data bus is used to transfer data between the memory and the CPU.
7. The data bus is bidirectional and the address bus is unidirectional. The control bus controls both read and write operations.
8. The read operation fetches data from memory and transfers to MDR. A single control line performs two operations like Read/Write using 1 or 0.
9. Also, the write operation transfers data from the MDR to memory. This organisation is shown below.

10. The word in the RAM has the same size (no.of bits) as the Memory Data Register (MDR). If the processor is an 8-bit RAM processor like Intel 8085, its MDR and the word in the both have 8 bits.
11. If the size of the MDR is eight bits, which can be connected with a word in the memory which is also eight bits size. The data bus has eight parallel wires to transfer data either from MDR to word or word to MDR based on the control(Read or write).

13. This control line is labeled as which becomes 1 means READ operation and 0 means WRITE operation. 

14. These pictures show the contents of MDR and the word before and after the READ operation.
i. The read operation transfers the data(bits) from word to Memory Data Register.
ii. The write operation transfers the data(bits) from Memory Data Register to word.