Tags: #◇Computer Science #◇CSARCH1 #◇Computer Architecture #◇Data Representation #◇Binary Codes for Decimal Digits

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Binary Codes for Decimal Digits

◇Overview

This module covers how to represent decimal digits using different types of binary codes. Representing decimal digits in binary requires a minimum of 4 bits per digit, allowing for $2^4 = 16$ combinations. Since there are only 10 decimal digits, 6 combinations remain unused.

◇Types of Binary Codes

1. Binary Coded Decimal (BCD):
   • Weighted code (8 4 2 1).
2. 2421 Code:
   • Weighted code (2 4 2 1).
   • Self-complementing: The 9's complement of a decimal digit is obtained by flipping the bits of its binary code.
3. Excess-3 Code:
   • Derived by adding 3 (0011 in binary) to the BCD representation.
   • Self-complementing code.
4. 8, 4, -2, -1 Code:
   • Weighted code with positive and negative weights.
   • Self-complementing code.
5. Biquinary Code (5 0 4 3 2 1 0):
   • 7-bit code with error-detection properties.
   • Contains a two-bit group (5 0) and a five-bit group (4 3 2 1 0).

◇Gray Code (Reflected Code)

• A non-weighted binary code where only one bit changes in the sequence when going from one number to the next.
• Useful in electro-mechanical applications such as rotating motors to avoid transient errors during state transitions.

Decimal Digit Representations Table

◇Examples

• Representing 395:
  • BCD: 0011 1001 0101
  • 2421: 0011 1111 1011
  • Excess-3: 0110 1100 1000
  • 8, 4, -2, -1: 0101 1111 1011

◇References & Navigation

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