Printed Ldn 2010 Unit 08 b&w

XOR XNOR AND-OR-INV (Parity) : BCD, Excess-3 Gray

: Wakerly 5.8.1, 5.8.2, 5.8.3, 5.9, 5.9.1, 2.10, 2.11, 2.15.1, 5.4.8

Mano 1.7, 3.8, 3.9, 4.8

= +

EXCLUSIVE-OR (XOR)X Y XY0 0 0 0 1 11 0 11 1 0

1 10

X

AND-OR

X

NAND

X(X+Y)+Y(X+Y) =XX++YX+Y = + =

() = +

EXCLUSIVE-NOR (XNOR)

X Y (XY)0 0 10 1 01 0 0 1 1 1

()100

X

()

AND-OR

OR & XNORX

()

AND-OR

X

()

AND/NOR

X

()

X

()

NAND/OR

XOR & XNOR

0 = 1 = X = 0 X = 1 Y = Y = ( ) Y = ( )

Y = Y X( Y) Z = (Y Z) = Y Z

XOR & XNOR

()

()

()

()

Z = Z + Z + Z + Z

XOR 3

()Z10

X

Z

AND-OR

01

010

101

00 01 11 100

1

1 10Z

Z

(Z) = Z + Z + Z + Z

XNOR 3

(()Z)10

X

(Z)

AND-OR

01

010

101

00 01 11 100

1

1 00Z

Z

AND-OR-INVAND-OR-INV:

NAND

X

Z

Z

AND-OR-INV

X

(Z)

Z

AND-OR-INV

NAND

(Parity Code)

0101

000001010011100101

PoddXYZ

01

10

110111

1010

000001010011100101

PevenXYZ

10

01

110111

, (parity bit) ,

1

Z

..P

0

Z

..

(odd parity) m : 1, 1 0, 1

m-1 R

10 1

0Z

1

W 0

1

10 1

0Z1

W 0 0 m=4

ODD ODD

(even parity) m : 1, 1 0, 1

m-2 R 1 XNOR ( )

10

1

0Z

1

W 1

1

10 1

0Z1

W 1 1 m=4

EVEN EVEN

(m ) : 0,

(. 1) 1,

(. 1) ( m-2 R 1 R). ( = 1) .

m=4

10

1

0Z

1

Podd1

1

10 1

0ZPodd

0 0

0

EVEN EVEN

10 1

0Z

1

Peven0

1

10 1

0Z0

Peven1 1

(m ) : 0,

(. 1) 1,

(. 1) ( m-1

R). ( = 1) .

m=4

ODD ODD

Podd m-1 ( m-3 R 1 XNOR),

m 0

100Z

0 Podd0

00 0

0Z0 0

1 PoddEVEN

EVEN

3 4 , 3 0.

Peven m-1 ( m-2 R)

m 0

000Z

0 Peven0

00 0

0Z0 0

0PevenODD

ODD

3 4 , 3 0.

MSI : 74x280 & 9

8

9

10

11

12

13

1

2

4

5

6EVEN

ODD

MSI : 74x280 & 9

8

9

10

11

12

13

1

2

4

5

6

5 AND-OR-INV

BUFFEREDINPUTS

2 = (A1,A0) = (1,0) = , 1 = 1, 0 = 0

F(A=B) = (A1B1)y(A0B0)= (A1B1+A1B1)y(A0B0+A0B0) = A1B1(A0B0+A0B0) + A1B1(A0B0+A0B0) = A1A0B1B0 + A1A0B1B0 + A1A0B1B0 + A1A0B1B0*

> , 1 = 1, 1 = 0 1 = 1, 0 = 1, 0 = 0 F(A>B) = A1B1 + (A1B1)yA0B0

= A1B1 + A0B1B0 + A1A0B0* ( )

< , 1 = 0, 1 = 1 1 = 1, 0 = 0, 0 = 1 F(A

4 (=)

= (A3,A2,A1,A0) = (3,2,1,0)

=, 3=3, 2=2, 1=1, 0=0 F(A=B) = (A3B3)y(A2B2)y(A1B1)y(A0B0)

4 (>)

= (A3,A2,A1,A0) = (3,2,1,0)

A>B, 3=1, 3=0 3=3, 2=1, 2=0 3=3, 2=2, 1=1,1=0 3=3, 2=2, 1=1, 0=1,0=0

F(A>B) = A3B3+(A3B3)A2B2+(A3B3)(A2B2)A1B1+(A3B3)(A2B2)(A1B1)A0B0

4

3

3

2

2

1

1

0

0 F(A=B)

F(AB)

BCD(Binary-Coded-Decimal)

2345

6000000010010001101000101

89

0110011110001001

=10 BCD

10

7

=10 BCD

15

1 1 1 1

0 1 0 1 BCD0 0 0 1

BCD 4 0 9. BCD 8-4-2-1

1 5

Excess-3

2345

6001101000101011001111000

89

1001101010111100

=10 Exc-3

10

7

=10 Exc-3

15

1 1 1 1

1 0 0 0 Excess-30 1 0 0

Excess-3 4 0 9. BCD 3.

- 9 1 0 0 1.

1 5

8.1

BCD excess-3 : =(,B,C,D) : E=(W,X,Y,Z)

A={0,1,..,8,9}E={3,4,..,11,12}

E=A+3

AND-OR, OR-AND, NAND-NAND NOR-NOR 2

8.2

1 BCD, BCD+1

: BCD = (D0,C0,B0,A0) : BCD+1mod10 = (D1,C1,B1,A1)

BCD = {0,1,..,8,9}BCD+1mod10 ={1,2,..,9,0}

AND-OR, OR-AND, NAND-NAND NOR-NOR 2

8.3

()

BCD (segment).

F BE C

G

D

GrayGrayg2 g1 g0

23456

000001011010110111101

000001010011100101110

=10

10

7 100111

=2b2 b1 b0

Gray 3 (g2,g1,g0) 3 (b2,b1,b0) :- b1=b0, g0=0, g0=1.

- b2=b1, g1=0, g1=1.

- g2=b2 Gray . Gray .

Gray

2

001 011

001 010

=10

Gray

1

ADCs, , 1.

.

000, 011

:

8.4

Gray.

Gray .( 4 )

XOR

8.5

BCD Gray. XOR,

.

8.3

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Printed Ldn 2010 Unit 08 b&w