logic gates. outline logic gates the inverter the and gate the or gate the nand gate the nor...

Logic Gates

Outline

Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate

Drawing Logic Circuit Analysing Logic Circuit

Outline

Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate

Drawing Logic Circuit Analysing Logic Circuit

Logic Gates Gate Symbols

EXCLUSIVE OR

a

ba.b

a

ba+b

a a'

a

b(a+b)'

a

b(a.b)'

a

ba b

a

ba.b&

a

ba+b1

AND

a a'1

a

b(a.b)'&

a

b(a+b)'1

a

ba b=1

OR

NOT

NAND

NOR

Symbol set 1 Symbol set 2

(ANSI/IEEE Standard 91-1984)

Logic Gates: The Inverter

The Inverter

A A'

0 1 1 0

A A' A A'

Application of the inverter: Complement.

1

0

0

1

0

1

0

1

1

0

0

1

1

0

1

0

Binary number

1’s Complement

Logic Gates: The AND Gate (1/2)

The AND Gate

A B A . B0 0 00 1 01 0 01 1 1

A

BA.B

&A

BA.B

Logic Gates: The AND Gate (2/2)

Application of the AND Gate

1 sec

A

1 secEnable

A

EnableCounter

Reset to zero between Enable pulses

Register, decode and frequency display

Logic Gates: The OR Gate

The OR Gate

1

A

BA+B

A

BA+B

A B A + B0 0 00 1 11 0 11 1 1

Logic Gates: The NAND Gate

The NAND Gate

&A

B(A.B)'

A

B(A.B)'

A

B(A.B)'

NAND Negative-OR

A B (A.B)'0 0 10 1 11 0 11 1 0

Logic Gates: The NOR Gate

The NOR Gate

NOR Negative-AND

1

A

B(A+B)'A

B(A+B)'

A

B(A+B)'

A B (A+B)'0 0 10 1 01 0 01 1 0

Logic Gates: The XOR Gate

The XOR Gate

=1A

BA B

A

BA B

A B A B0 0 00 1 11 0 11 1 0

Logic Gates: The XNOR Gate

The XNOR Gate

A

B(A B)'

=1A

B(A B)'

A B (A B) '0 0 10 1 01 0 01 1 1

Outline

Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate

Drawing Logic Circuit Analysing Logic Circuit

Drawing Logic Circuit (1/2)

When a Boolean expression is provided, we can easily draw the logic circuit.

Examples:

(i) F1 = x.y.z' (note the use of a 3-input AND gate)

xy

z

F1

z'

Drawing Logic Circuit (2/2)

(ii) F2 = x + y'.z (if we assume that variables and their complements are available)

(iii) F3 = x.y' + x'.z

x

y'z

F2

y'.z

x'z

F3

x'.z

x.y'xy'

Outline

Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate

Drawing Logic Circuit Analysing Logic Circuit

Analysing Logic Circuit

When a logic circuit is provided, we can analyse the circuit to obtain the logic expression.

Example: What is the Boolean expression of F4?

A'.B'

A'.B'+C (A'.B'+C)'

A'

B'

CF4

F4 = (A'.B'+C)' = (A+B).C'