Design of Fast Adders

Introduction

• Presenter: Atik
• Topic: Design of Fast Adders

Basic Concepts

• Binary Numbers: Computer language is binary, represented as 0s and 1s.
• BCD (Binary Coded Decimal): Another representation used by computers to store numbers.

Conversion from Binary to BCD

• Explanation of converting binary numbers to BCD using examples.
• Consider decimal numbers from 0 to 19.
  • Example: Decimal 0 to 9: BCD and binary representation are the same.
  • Example: Decimal 10 to 19: BCD and binary representation differ.

Representation Details

• BCD Representation: Uses separate bits for each decimal digit.
• Bits Used:
  • BCD bits: S1, S2, S4, S8, and carry bit C.
  • Binary bits: Z1, Z2, Z4, Z8, and carry bit K.

Key Observations

• For decimal numbers 0-9:
  • BCD representation = Binary representation.
• For decimal numbers 10-19:
  • BCD representation differs from binary representation.
  • Example: 10 in binary is different from BCD.

Fast Adders

• Purpose: To take binary sum as input and convert it to BCD.
• Formula for Carry Bit (C):
  • C = K + (Z8 * Z4) + (Z8 * Z2)

Fast Adder Mechanics

• Inputs:
  • Addend: 2
  • Augment: 3
• Binary representation of inputs: Z1, Z2, Z4, Z8, K.

Circuit Design

• Components:
  • Two AND gates
  • One OR gate
• Operation:
  • AND gates perform multiplication.
  • OR gate performs addition of results.

Output Generation

• Output from the OR gate = Carry bit C.
• Final output after addition: S1, S2, S3, S4, S8 (BCD bits).
• The carry bit is also included in the output.

Conclusion

• Summary of the conversion process from binary sum to BCD sum.
• Closing remarks: Presenter signs off and expresses hope that the concept is clear.