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Data Representation

The Binary System

  • The binary number system is a base 2 system that uses only two values: 0 and 1.

  • This system is fundamental for data representation in computers, as all forms of data (text, images, videos) can be encoded in binary.

Converting Binary to Denary

Example 1:

  • Binary: 11101110

  • Calculation: 128 + 64 + 32 + 8 + 4 + 2 = 238

Example 2:

  • Binary: 011110001011

  • Calculation: 1024 + 512 + 256 + 128 + 8 + 2 + 1 = 1931

Activities for Binary to Denary Conversion

  • Convert the following binary numbers:

    • a. 51

    • b. 127

    • c. 153

    • d. 116

    • e. 255

    • f. 15

    • g. 143

    • h. 179

    • i. 112

    • j. 238

    • k. 487

    • l. 1364

    • m. 3855

    • n. 1992

    • o. 2047

    • p. 31984

    • q. 16141

    • r. 49983

    • s. 34952

    • t. 32767

Converting from Denary to Binary

Method 1: Subtracting Powers of 2

  • Convert the denary number 142:

    • Break down as follows: 128 + 8 + 4 + 2

    • Resulting binary number: 10001110

Method 2: Successive Division by 2

  • Process:

    • Start with a denary number and divide by 2 repeatedly, documenting the quotient and the remainder until reaching zero.

Activities for Denary to Binary Conversion

  • Convert the following denary numbers:

    • a. 101001

    • b. 1000011

    • c. 1010110

    • d. 1100100

    • e. 1101111

    • f. 1111111

    • g. 10010000

    • h. 10111101

    • i. 11001000

    • j. 11111111

    • k. 1000000011101000

    • l. 1101111000

    • m. 111111111111

    • n. 100000000010000

    • o. 1111001101100011

The Hexadecimal System

  • The hexadecimal system is a base 16 system, using 0-9 and A-F.

  • Each hex digit corresponds to an integer from 0 to 15, where A=10, B=11, C=12, D=13, E=14, F=15.

Error Codes and Uses of Hexadecimal System

  • Hexadecimal system is utilized in various applications like IPv6 addresses, MAC addresses, and HTML color codes.

Character Sets – ASCII Code and Unicode

  • ASCII: 7-bit codes (0 to 127) representing English letters, numbers, and control characters.

  • Unicode: Supports characters from multiple languages, enables extensive character representation beyond ASCII (usually 1 to 4 bytes).

Sound Representation

  • Sound waves are analogue, requiring sampling for digital storage.

  • Sampling: measures amplitude at regular intervals, producing a digital representation of sound.

  • Sampling Resolution: refers to the number of bits per sample affecting sound quality.

  • Sampling Rate: measures the number of samples per second in hertz (Hz).

Image Representation

  • Bitmap images are made up of pixels, stored in a matrix. Resolution refers to the image's detail level, often quantified in DPI (dots per inch).

Data Storage and Compression

  • Data Compression: reduces file size to save space and expedite upload/download processes.

  • Two types of compression:

    • Lossy Compression: Permanently removes some data (e.g., MP3 for audio).

    • Lossless Compression: Allows original data to be perfectly reconstructed (e.g., PNG for images).

File Size Calculation and IEC Memory Size System

  • File Size Calculation: involves determining the memory needed to store files, following standards set by the IEC.

User Authentication and Security Measures

  • Various forms of authentication ensure data access integrity through passwords, two-step verification, and secure system updates.

  • Using firewalls and anti-malware to safeguard systems against attacks.

Programming Concepts for Software Development

  • Understanding variables, constants, control structures (sequence, selection, iteration), and function definitions contribute to effective program constructs.