Class Notes: Encoding Schemes and Number System

• Computers interpret keyboard inputs by mapping each key to a unique code, which is then converted into binary form.
• Computers understand only binary language (0s and 1s).

Example

• When you press the key ‘A’ on the keyboard:
  • It is mapped to the decimal value 65.
  • This decimal value is then converted to binary (1000001).

Encoding

• Encoding is converting data into an equivalent code using a specific scheme.
• Example: ‘A’ -> Decimal 65 -> Binary 1000001.
• Standard encoding schemes ensure consistent representation across different keyboards and systems.

ASCII (American Standard Code for Information Interchange)

• Developed in the 1960s to standardize character representation.
• Uses 7 bits to represent characters, allowing 128 different characters.
• Example: ASCII value for ‘D’ is 68, which is 1000100 in binary.

ISCII (Indian Script Code for Information Interchange)

• Developed in the 1980s for Indian languages.
• Uses 8 bits, allowing 256 characters, including 128 ASCII codes and additional Indian language characters.

UNICODE

• A universal encoding standard that includes characters from all languages.
• Provides a unique number for every character, regardless of the device or software.
• Common UNICODE encodings: UTF-8, UTF-16, UTF-32.

Number Systems

• Numbers can be represented in various systems: Decimal, Binary, Octal, and Hexadecimal.

Decimal Number System

• Base-10 system using digits 0-9.
• Example: 237.25 is computed as 2×102+3×101+7×100+2×10−1+5×10−22 \times 10^2 + 3 \times 10^1 + 7 \times 10^0 + 2 \times 10^{-1} + 5 \times 10^{-2}2×102+3×101+7×100+2×10−1+5×10−2.

Binary Number System

• Base-2 system using digits 0 and 1.
• Example: 1011.101 in binary.

Octal Number System

• Base-8 system using digits 0-7.
• Compact representation of binary numbers.
• Example: 237.05 in octal.

Hexadecimal Number System

• Base-16 system using digits 0-9 and letters A-F.
• Compact representation of binary numbers.
• Example: 23A.05 in hexadecimal.

Conversions Between Number Systems

• Decimal to Binary: Divide the number by 2, record remainders, and write in reverse order.
  • Example: 65 in decimal -> 1000001 in binary.
• Decimal to Octal: Divide the number by 8, record remainders, and write in reverse order.
  • Example: 65 in decimal -> 101 in octal.
• Decimal to Hexadecimal: Divide the number by 16, record remainders, and write in reverse order.
  • Example: 65 in decimal -> 41 in hexadecimal.