Combinational Circuit
Review
Combinational Circuit Design
Steps of designing Combinational circuits
1. Determine how many inputs and outputs are required
2. Describe the circuit function with Truth Table
3. Derive logical equation for each output using
1. Sum-Of-Products (SOP) or
2. Product-Of-Sum (POS)
4. Minimize the expression using one of the following methods
Algebraic rules
Karnaugh Map
Quine-McCluskey (which can be in the form of computer program
6. Implement (convert equations into equivalent logic gates)
Combinational Circuit Design Example
Design a half-adder (HA) circuit with two inputs (a,b) and two outputs sum
(S) and carry (C). The HA function is to perform binary addition to its input
a b C S
0 0 0 0
a S
HA 0 1 0 1
b C 1 0 0 1
1 1 1 0
Synchronous & Asynchronous Systems
• Digital circuits can operate in asynchronous or
synchronous mode
• Asynchronous - The time at which a change occurs in
one circuit has no relation to the time a change occurs
in another circuit (not synchronized)
• Synchronous - In this mode, all circuits in the system
change their state at some precisely defined instants
• The clock signal in a digital system provides such a
global definition of time instants at which changes can
take place.
• The clock signal also specifies the speed at which a
circuit can operate.
Clock Signal
• A clock is a sequence of 1s and 0s
• We refer to the period during which the clock is 1 as
the ON period and the period with 0 as the OFF period
• The clock signal edge going from 0 to 1 is referred to
as the rising edge (positive edge)
• The clock signal edge going from 1 to 0 is referred to
as the falling edge (negative edge)
Clock Signal
• A clock cycle/period “T ” is defined as the time between
two successive rising (or falling) edges
• Clock rate or frequency “f ” is measured in number of
cycles per second (Hz)
• The clock signal serves two distinct purposes in a
digital circuit where it provides
— The global synchronization signal for the entire system
— Timing information in the form of a clock period
Sequential Elements (Latch & Flip Flop)
• Latches/Flip-Flops are the basic elements of sequential
systems
• Latch or flip-flop represents 1-bit memory
• Latches are level-sensitive devices in that the device
responds to the input signal levels (high or low).
• In contrast, flip-flops are edge-triggered. That is,
output changes only at either the rising or falling edge
S-R Latch using NOR Gates
S-R Latch using NOR Gates
Set
S-R Latch using NOR Gates
No Change
S-R Latch using NOR Gates
Reset
S-R Latch using NOR Gates
No Change
S-R Latch using NOR Gates
Not used
S-R Latch using NOR Gates
THIS GATE IS
FASTER
No Change
S-R Latch using NOR Gates
No Change
S-R Latch Symbol and Truth Table
No
Change
Reset
Set
Hazard
•
S-R Latch As a 1-bit Memory
• Latch has the capability to store a bit
• To write 1 into this latch, set SR as 10
• To write 0, use SR = 01
• To retain a stored bit, keep both S and R inputs at 0
• Avoid setting SR to 11
• Once we have the design to store a single bit, we can
replicate this circuit to store more bits or bytes.
Clocked S-R Latch
•How to make S-R latch synchronized
— Output changes at specific instants
•Adding clock to gate the inputs to provide synchronization
•Now it is called clocked S-R Latch
Clocked S-R Latch
Clocked S-R Latch
Clocked S-R Latch
Clocked S-R Latch
Clocked S-R Latch
D - Latch
• A problem with SR latches is that we have to avoid the
SR = 11 input combination
• This problem is solved by the D latch
D – Latch Operation
D – Latch Operation
D – Latch Operation
D – Latch Operation
D – Latch Operation
D – Latch Operation
D – Latch Operation
D – Latch Truth Table
FLIP FLOPS
• Flip-flops are edge-triggered devices whereas latches
are level sensitive
• Some manufacturers do not follow this distinction
• How edge triggering can be achieved ?
• One solution is to use Master-Slave Technique
• Note the difference between D-latch and D-FF symbols
Latch FF +edge FF -edge
Master – Slave FF
Master Slave
Master – Slave FF
Master Slave
Master – Slave FF
Master Slave
Master – Slave FF
Master Slave
Master – Slave FF
Master Slave
Master – Slave FF
Master Slave
J-K FLIP FLOP
• It is another type of Flip-Flops that makes the avoided
input combination “SR”=11 useful
• J-K Flip-Flop uses a 2nd feedback as shown
J-K FLIP FLOP Truth Table
No
Change
Reset
Set
Toggle
J-K FLIP FLOP Example
CL
K
Q
N N
S R T T T T
C C
