Examples demonstrating how the circuit in figure 6...,bnnnn adds and subtracts

General
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examples demonstrating how the circuit in figure 6…,bnnnn adds and subtracts

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I’m sorry, but I can’t see figure 6 as mentioned. However, I can help you understand how basic circuits add and subtract.

Addition and Subtraction with Circuits

1. Binary Addition

Half Adder:

  • Purpose: Adds two single binary digits.
  • Components: XOR gate for sum, AND gate for carry.
  • Operation:
    • Sum: XOR of the two bits.
    • Carry: AND of the two bits.

Full Adder:

  • Purpose: Adds three single binary digits (including carry from previous).
  • Components: Two XOR gates, two AND gates, and one OR gate.
  • Operation:
    • Sum: XOR of the input bits and incoming carry (A \oplus B \oplus C_{in}).
    • Carry: A \cdot B + (A \oplus B) \cdot C_{in}.

2. Binary Subtraction

Half Subtractor:

  • Purpose: Subtracts two single binary digits.
  • Components: XOR and AND (with NOT) gates.
  • Operation:
    • Difference: XOR of the two bits.
    • Borrow: NOT(A) AND B.

Full Subtractor:

  • Purpose: Subtracts two binary digits with borrow.
  • Components: Two XOR gates, three AND gates, and two OR gates.
  • Operation:
    • Difference: XOR of the input bits and incoming borrow.
    • Borrow: B \cdot \overline{A} + (A \oplus B) \cdot B_{in}.

Example:

  • Adding 1 + 1:

    Half Adder results in:

    • Sum = 0
    • Carry = 1

  • Subtracting 1 from 2 (Binary 10 - 01):

    Full Subtractor results in:

    • Difference = 1
    • Borrow = 0

Summary: Basic circuits like adders and subtractors perform addition and subtraction using logical gates such as XOR, AND, OR, and NOT. Half and full versions handle simple operations and those requiring carry or borrow bits, respectively. Let me know if you have specific components or a diagram to discuss!