Second Semester_Digital Logic_Introduction to Digital System

 

1.1 Introduction to Analog and Digital Systems

• Analog Systems: Continuous signals, infinite possible values.

  • Examples: Temperature sensors, microphones.

• Digital Systems: Discrete signals, limited set of values (usually 0 and 1).

  • Examples: Computers, digital clocks.

• Key Difference: Accuracy, noise tolerance, and ease of storage/processing.

---

1.2 Features of Digital Systems

• Reliability: Less prone to noise.

• Precision: Exact values represented in binary.

• Storage and Processing: Easier with binary data.

• Programmability: Digital systems can be reprogrammed for different tasks.

---

1.3 Number Systems

• Decimal (Base 10): 0–9

• Binary (Base 2): 0–1

• Octal (Base 8): 0–7

• Hexadecimal (Base 16): 0–9, A–F

• Conversions:

  • Binary ↔ Decimal

  • Binary ↔ Octal

  • Binary ↔ Hexadecimal

---

1.4 Binary Arithmetic and Complement Systems

• Binary Arithmetic: Addition, subtraction, multiplication, division in base 2.

• Complement Systems: Used for subtraction.

  • 1’s Complement: Invert all bits.

  • 2’s Complement: 1’s complement + 1

  • 9’s Complement: For decimal subtraction

  • 10’s Complement: 9’s complement + 1

• Advantage: Simplifies subtraction to addition.

---

1.5 Codes

• BCD (Binary Coded Decimal): Each decimal digit represented in 4-bit binary.

• XS-3 (Excess-3): BCD + 3, used in decimal arithmetic.

• Gray Code: Only one bit changes between consecutive numbers.

• Hamming Code: Error detection and correction.

• Alphanumeric Codes: Represent characters digitally.

  • ASCII (7 or 8 bits), EBCDIC (8 bits), UNICODE (16 or 32 bits).

---

1.6 Error Detecting and Error Correcting Codes

• Parity Bits: Single-bit detection (even/odd parity).

• Checksums & CRC: Detect burst errors in data transmission.

• Hamming Code: Detects and corrects single-bit errors.

• Importance: Ensures reliable data communication and storage.