Unit 2: Number Systems — Short Questions

Ans

Human's View about Memory | Code in Decimal | Code in Binary | Address
'P' | 80 | 01010000 | 7003
'h' | 104 | 01101000 | 7004
'o' | 111 | 01101111 | 7005
'n' | 110 | 01101110 | 7006
'e' | 101 | 01100101 | 7007

Ans A number system is the system for representation of numeric data. A Number system is defined as a set of values used to represent different quantities. We all are familiar with decimal number system where each number consists of digits from 0 to 9. In a computer system, other number systems are also used. e.g. Binary, Hexadecimal etc.

Ans. A process to convert one number system to another number system is called conversion of number system. For example, converting a decimal number to binary number.

Ans Digital computers store data in binary form. It means that whether it is a text, picture, movie or some application, it is stored in computer's memory in the form of 0s and 1s.

Ans. ASCII (American Standard Code for Information Interchange) is one such coding scheme published by ISO (International Standards Organization). It is 7-bit coding scheme. The codes are assigned to various characters. Most computers also use 8-bit ASCII code.
Example: A = 65, B = 66 and a = 97 etc.

Ans Bit stands for Binary Digit. A bit is the smallest unit of data and has value 1 or 0 representing ON or OFF state.
Computer understands only machine language, which consists of binary codes 0 and 1. So binary number system is very important for our computer.

Ans. A collection of 8 bits is called a byte. It is a set of bits, which represents a particular character or symbol. In memory one byte can store only one character.

Solution

Character | Decimal Code | Binary code
2 | 50 | 00110010
+ | 43 | 00101011
2 | 50 | 00110010
= | 61 | 00111101
4 | 52 | 00110100

So the message in ASCII is 00110010 00101011 00110010 00111101 00110100

Ans.

Hexa-Decimal | Binary
A | 1010
B | 1011
C | 1100
D | 1101

ABCD16 = (1010101111001101)2

Ans.

Binary | Hexa-decimal
1001 | 9
0110 | 6
0100 | 4
0110 | 6
0001 | 1

(0010110010001101001)2 = (16469)16

Ans.
0B9(16) = 0 x 16² + B x 16¹ + 9 x 16⁰
= 0 x 16² + 11 x 16¹ + 9 x 16⁰
= 0 x 256 + 11 x 16 + 9 x 1
= 0 + 176 + 9
= 185(10)

Ans. The octal numbering system is a base-8 number system that uses digits from 0 to 7. Each digit Represents a power of 8. In octal, the place values from right to left are 8⁰, 8¹, 8², and so on. For example, the octal number 157 means:
1x8²+5x8¹+7x8⁰=64+40+7=111(10)

Ans.
= 1 x 2⁵ + 0 x 2⁴ + 0 x 2³ + 0 x 2² + 0 x 2¹ + 0 x 2⁰
= 32 + 0 + 0 + 0 + 0 + 0
= (32)10

Ans.
= C x 16³ + 9 x 16² + 2 x 16¹ + 1 x 16⁰
= 12 x 16³ + 9 x 16² + 2 x 16¹ + 1 x 16⁰
= 12 x 4096 + 9 x 256 + 2 x 16 + 1 x 1
= 49152 + 2304 + 32 + 1
= (51489)10

Ans Encoding is the conversion of data from one format or representation to another, usually for storage, transport, or processing. To put it simply, it converts information into a format that computers, devices, or software can understand, transfer, or store.

Ans The major distinction between signed and unsigned integers is their capacity to represent both positive and negative numbers. Here's a clear contrast between the two.
Signed Integer: Can represent both positive and negative numbers, including zero.
An unsigned integer can only represent non-negative values.

Ans In computers, real values (also known as floating-point numbers) are used to represent numbers that have fractions or decimal points. These values are stored using IEEE standard, where each standard is represented by:
i. Sign bit
ii. Exponent
iii. Mantissa

Ans Binary arithmetic refers to the operations of addition, subtraction. Multiplication and division performed on binary numbers. Binary numbers are the basis of all operations in digital computers. Binary arithmetic operations are similar to decimal operations but follow binary rules.

Ans

• 0+0=0
• 0+1=1
• 1+0=1
• 1+1=0

Ans Booth's Algorithm: This algorithm is efficient for multiplying binary numbers, especially when dealing with large numbers or numbers with many consecutive similar bits.

Ans. The central processing unit (CPU) of a computer performs millions of binary multiplications every second to execute complex instructions and run programs.

Ans. Here are some of the most common text encoding schemes used in computers:

• ASCII (American Standard Code for Information Interchange)
• Extended ASCII
• Unicode (Universal Code)
• UTF-8 (Unicode Transformation Format-8)
• UTF-16 (Unicode Transformation Format-16)
• UTF-32 (Unicode Transformation Format-32)

Ans. Images are made up of tiny dots called pixels. Each pixel has a color, and the combination of all these pixels forms the complete picture. Computers store images using numbers to represent these colors.

Ans. A pixel (Picture Element) is the smallest unit of a digital image or display that may be independently manipulated for color and brightness. Pixels are the fundamental components of all digital images and screens, including those on smartphones, computers, and televisions.

Ans. In a color image each pixel's color can be represented by three numbers: Red, Green, and Blue (RGB). Each of these numbers typically ranges from 0 to 255. For Example, a pixel with RGB values (255,0,0) will be bright red.

Ans. JPEG (Joint Photographic Experts Group): Common format for photos. It compresses the image to save space but might lose some quality.
PNG (Portable Network Graphics): Supports transparency and maintains high quality without losing data.
GIF (Graphics Interchange Format): Used for simple animations and images with few colors.

Ans. Audio files are stored by capturing sound waves and converting them into digital data. This process involves sampling and quantization.

Ans. MP3 A common format that compresses audio to save space but may lose some quality.
WAV: Uncompressed format that maintains high quality.
AAC: Used by many streaming services for high-quality audio with efficient compression.

Ans. The number of frames shown per second, measured in frames per second (fps). Common frame rates are 24 fps (use in movies) and 30 fps (used in TV). Higher frame rates result in smoother motion in videos.

TV Stands for Television

Ans. Hard Drives (HDD) Use spinning disks to read/write data. They offer large storage capacities.
Solid State Drives (SSD): Use flash memory for faster access times and better performance.
Cloud Storage: Storage files on remote servers accessible via the internet, providing flexibility and backup.