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

'' YXYXYX

'')'( YXYXYX

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, 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-6.10-6.11