Download Boolean Algebra and logic gates

BOOLEAN ALGEBRA AND LOGIC
GATES
Chapter2-Lecture5
AGENDA

SOP and POS

Digital logic gates

Digital logic families
SOP AND POS

Determine if the following are POS or SOP:
(A+B’+C)(A+B’)(B+C’)
A’BC + AB’C + BC
POS
SOP
EXERCISE 1 :

Write a Boolean SOP expression for this truth table,
then simplify that expression as much as possible,
and draw a logic gate circuit equivalent to that
simplified expression:
A
B
C
F
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
SOLUTION:

Original SOP: F = A’BC’ + ABC’
= BC’(A’+A)
= BC’
B
C
since A + A’ = 1
F
EXERCISE 2: WRITE SOP AND POS
A
B
C
F
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
POS :
1
0
0
0
(F’)’ = (A’B’C+A’BC+AB’C’+ABC)’
1
0
1
1
1
1
0
1
1
1
1
0
SOP :
F = A’B’C’ + A’BC’ + AB’C + ABC’
= A’C’(B’+B) + A(B’C + BC’)
= A’C’ +A(B
C)
Next slide
= (A’B’C)’(A’BC)’(AB’C’)’(ABC)’
= (A+B+C’)(A+B’+C’)(A’+B+C)(A’+B’+C’)
DIGITAL LOGIC GATES
inverter
MORE GATES
Buffer F = X
X
F
X
F
MORE GATES
F = AB’ + A’B
= A
B
MORE GATES
F = AB + A’B’
= (A
B)’
NOTES:
All the gates except the inverter and buffer can be
extended to have more than 2 inputs.
 The multi-input gate have the same properties of the
2 input gate.
Example: x + y = y + x commutative
(x + y) + z = x + (y + z) = x + y + z associative
 NOR NAND operators are not associative
 NOR :
 i.e.( x y) z = x ( y z )
( x y) z = [(x + y)’ +z ]’ = (x + y)z’ = xz’ + yz’
x ( y z ) =[ x + (y + z)’]’ = x’(y + z)= x’y + x’z

DEFINITIONS:

NOR :
x
y z = (x + y + z)’

NAND :
x
y z = (xyz)’
DIGITAL LOGIC FAMILIES :

1.
2.
3.






Digital integrated circuits can be classified by:
Complexity
Logical operation
Circuit technology (digital logic family)
Basic circuit in each technology NAN,NOR, or
inverter gate.
The most popular families:
TTL: transistor-transistor logic
ECL: emitter-coupled logic
MOS: metal-oxide semiconductor
CMOS: complementary metal-oxide semiconductor
MAIN FEATURE OF EACH:

TTL: the standard logic family for a long time

ECL: useful for systems that require high speed
operation.

MOS: suitable for circuits that need high
component density

CMOS: for systems requiring low-power
consumption such as digital camera.