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Mastering XOR, XNOR, & Binary Adders: Logic Design and Implementation

This presentation covers the basic functions and applications of XOR and XNOR gates in logic design, along with detailed explanations on how XOR and XNOR gates are used to implement combinatorial logic and adders. The presentation also demonstrates the design and implementation of half adders, full adders using SSI and MSI logic, cascading single-bit adders to create multi-bit adders, and Boolean algebra simplification in adder circuits. Additionally, it compares XOR and AOI gate implementations for the sum function in full adders. The content includes examples, logic circuit designs, and step-by-step guidance on various aspects of XOR, XNOR, and binary adders.

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Mastering XOR, XNOR, & Binary Adders: Logic Design and Implementation

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  1. XOR, XNOR, & Binary Adders

  2. XOR, XNOR & Adders This presentation will demonstrate • The basic function of the exclusive OR (XOR) gate. • The basic function of the exclusive NOR (XNOR) gate. • How XOR and XNOR gates can be used to implement combinational logic design. • How XOR gates can be using to design half and full adders. • How full adders can be implemented with Small Scale Integration (SSI) and Medium Scale Integration (MSI) logic. • How single bit half and full adders can be cascaded to make multi-bit adders.

  3. XOR Gate – Exclusive OR X Y

  4. XNOR Gate – Exclusive NOR X Y

  5. Logic Design with XOR & XNOR • Example • Algebraically manipulate the logic expression for F1 so that XOR and XNOR gates can be used to implement the function. Other AOI gates can be used as needed.

  6. Logic Design with XOR & XNOR Solution

  7. Binary Addition Single Bit Addition: Carry Multiple Bit Addition: Cin Cout A B Sum

  8. Two Types of Adders Half Adder Full Adder 3 Inputs (A, B, Cin) 2 Outputs (Sum & Cout) Used for all other bits • 2 Inputs (A & B) • 2 Outputs (Sum & Cout) • Used for LSB only Sum Cout Sum Cout Full Adder Half Adder A B Cin A B

  9. Half Adder – Design

  10. Half Adder - Circuit

  11. Full Adder – Design of Cout

  12. Full Adder – Design of Sum K-Mapping did NOT help us simplify . . . Let’s try Boolean algebra.

  13. Boolean Simplification of Sum

  14. Full Adder - Circuit

  15. Full Adder: AOI vs. XOR Though XOR gates can be used for implementing any combinational logic design, their primary application is adder circuits. Compare the AOI implementation (above) for the sum function to the XOR implementation (below).

  16. MSI Full Adder SSI - Full Adder MSI - Full Adder

  17. Cascading Adders – Four Bits Example: 6 + 3 = 9 General Form

  18. Four Bit Adder with SSI Logic Full Adder Full Adder Full Adder Half Adder

  19. Four Bit Adder with MSI Logic Full Adder Full Adder Full Adder Full Adder

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