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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.