ECE 3110: Introduction to Digital Systems Chapter 6 Combinational Logic Design Practices XOR, Parity Circuits, Comparators.

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ECE 3110: Introduction to Digital Systems Chapter 6 Combinational Logic Design Practices XOR, Parity Circuits, Comparators

2 Exclusive OR and Exclusive NOR Gates XOR : XNOR : Truth Table : XOR X Y XOR XNOR 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 XOR X Y F X Y F

3 XOR and XNOR Symbols Equivalent Symbols of XOR gate Equivalent Symbols of XNOR gate Any 2 signals (inputs or outputs) may be complemented without changing the resulting logic function

4 SSI XOR and XNOR 74x86 : 4 XOR gates 74x266: 4 XNOR gates with “open collector” or “open drain” output

5 XOR Application: Parity Circuit Odd Parity Circuit : The output is 1 if odd number of inputs are 1 Even Parity Circuit : The output is 1 if even number of inputs are 1 Example : 4-bit Parity Circuit Daisy-Chain Structure Tree structure Input : 1101 Odd Parity output : 1 Even Parity output : 0 I0 I1 I2 I3 ODD EVEN I0 I1 I2 I3 ODD EVEN

6 MSI Parity Circuit : 74x280

7 Parity-Checking Application: memory

8 Comparators Compares Two binary words and indicate if they are equal Magnitude Comparators : A Comparator A=B? B A Comparator A=B B A>B A { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/12/3378286/slides/slide_8.jpg", "name": "8 Comparators Compares Two binary words and indicate if they are equal Magnitude Comparators : A Comparator A=B.", "description": "B A Comparator A=B B A>B A

9 Equality Comparators 1-bit comparator 4-bit comparator EQ_L

10 Iterative Comparator

11 Multi-bit Iterative Comparator

12 MSI Comparator : 74x85 4 bit comparator 3 outputs : A=B, A B 3 Cascading inputs Functional Output equations : (A>B OUT)= (A>B)+(A=B).(A>B IN) (AB IN) =0 (ABIN ABOUT

13 8 bit Comparator B0 A1 B1 A2 B2 A3 A0 B3 74x85 ABIN ABOUT B0 A1 B1 A2 B2 A3 A0 B3 74x85 ABIN ABOUT B0 A1 B1 A2 B2 A3 A0 B3 B4 A5 B5 A6 B6 A7 A4 B7 +5V AB Most Significant bitsLeast Significant bits

14 8-bit Magnitude Comparator

15 Other conditions