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 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<B

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) (A<B OUT)= (A<B)+(A=B).(A<B IN) (A=B OUT)= (A=B).(A=B IN) Cascading inputs initial values : (A=B IN) =1 (A>B IN) =0 (A<B IN) =0 B0 A1 B1 A2 B2 A3 A0 B3 74x85 A<BIN A=BIN A>BIN A<BOUT A=B OUT A>BOUT

13 8 bit Comparator B0 A1 B1 A2 B2 A3 A0 B3 74x85 A<BIN A=BIN A>BIN A<BOUT A=B OUT A>BOUT B0 A1 B1 A2 B2 A3 A0 B3 74x85 A<BIN A=BIN A>BIN A<BOUT A=B OUT A>BOUT B0 A1 B1 A2 B2 A3 A0 B3 B4 A5 B5 A6 B6 A7 A4 B7 +5V A<B A=B A>B Most Significant bitsLeast Significant bits

14 8-bit Magnitude Comparator

15 Other conditions

16 Next… Adders, subtractors, ALUs Reading Wakerly CH