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Provides a detailed overview of different types of adders, their construction, and their applications in digital circuits.

Objectives

  • Introduction to adders
  • Explanation of half adders and full adders with circuit diagrams
  • Simplification of Boolean expressions for full adders
  • Overview of four-bit adders, serial binary adders, parallel binary adders, and 8421 BCD adders

Introduction

  • Addition at the digital logic level is performed in binary.
  • Special circuits called adders are used for addition operations.
  • Types of adders include half adders and full adders.

Half Adder

  • Adds two binary inputs and produces a sum bit and a carry bit.
  • Sum: ( \text{A} \oplus \text{B} ) (A XOR B)
  • Carry: ( \text{A} \cdot \text{B} ) (A AND B)
  • Truth table provided for half adder.

Full Adder

  • Takes into account the carry-in value.
  • Adds three bits (two inputs and a carry-in) and produces a sum bit and a carry-out bit.
  • Sum: ( \text{A} \oplus \text{B} \oplus \text{Cin} )
  • Carry-out: ( (\text{A} \cdot \text{B}) + (\text{Cin} \cdot (\text{A} \oplus \text{B})) )
  • Truth table provided for full adder.
  • Can be implemented using two half adders.

Four-Bit Adder

  • Constructed by cascading four full adders to form a four-bit adder.
  • Example provided with binary addition of two 4-bit numbers.

Serial Binary Adder

  • Adds two binary numbers serially, bit by bit.
  • Uses a clock signal to synchronize the addition process.
  • Steps for adding two numbers provided.

Parallel Binary Adder

  • Produces the arithmetic sum of two binary numbers.
  • Constructed with full adders connected in cascade.
  • Example provided with a four-bit parallel adder.

8421 BCD Adder

  • Adds two single decimal digits represented in 8421 BCD code.
  • If there is no carry, the sum is the binary sum of the two digits.
  • If there is a carry, the correct decimal number is determined by adjusting the binary sum.

Adders – Lesson 9

Engineering Institute of Technology