1 sequential digital circuits alexander titov 11 october 2014
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1
Sequential Digital CircuitsAlexander Titov11 October 2014
2Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
Layers of Abstraction in Computes Science (CS)
Application
Algorithms
Programming Language
Operating System
Instruction Set Architecture
Microarchitecture
Gates/Register-Transfer Level (RTL)
Circuits
Physics
Topics of this lecture
3Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
• But, combinational circuits have a significant limitation: they cannot remember any information
Refresher: Combinational vs. Sequential Circuits• If the output of a function is completely defined by
the current input then the function is called combinational:Qt = F(xt, yt, zt,
…)• Combinational circuit (scheme) is an implementation of a combinational function
• A lot of things can be implemented using combinational circuits• Just a few examples that we already know: summator,
decoder, multiplexer
• But, combinational circuits have a significant limitation:
4Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
Sequential Circuits
• Sequential circuits are able to store information
• If the output of a function depends not only on the current input, but on the previous state, then the function is called sequential
Qt = F(xt, yt, zt, …, Qt-
1)F(xt-1, yt-1, zt-1, …, Qt-2))
F(xt-2, yt-2, zt-2, …, Qt-3)))
• Sequential circuit is an implementation of a sequential function
• Their main advantage is ability to remember the previous state• Any circuit with memory is a sequential circuits
5Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
SR Flip-Flop
S R Qt-1 Qt
x y out
0 0 1
0 1 0
1 0 0
1 1 0
Q
!Q
xy
out
yout
≡
xy
out
0≡
out
Q
!Q
reset
set
0
0
1 0
11
0
1
NOR:
SR flip-flop:
o The simplest store element:
o SR flip-flop:
0 1
0 0 Q Q
0 1 Q 0
1 0 Q 11 1 Q 0
reset
set
Q
!Q
Prohibited state
6Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
SR Flip-Flopreset
set
Q
!Q
R
!QS
QS R Qt-1 Qt
0 0 Q Q
0 1 Q 0
1 0 Q 1
1 1 Q 0
S0
1
R0
1
Q0
1
!Q0
1
?
?
But, which signal will be really faster will depend on many factors (e.g., temperature).
The output will be determined by the fastest signal
7Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
D Flip-Flop
• Don’t have prohibited states• Asserted by a level of the write enable signal (we)• Store one bit of information• Can be used as building block for creating static memory
arrays
S
QR
!Q
Write enable
DataD
we
QD we Qt-1 Qt
D 0 Q Q
0 1 Q 0
1 1 Q 1
9Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
Single port 2^MxN Memory Array
MemoryArray
address
input data output data
M
N N
Write enable
10Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
Single port 4x1 Memory Array
MemoryArray
address
input data output data
2
1 1
Write enable
11Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
Single port 4x1 Memory Array
De
Q De
Q De
QDe
Q
S0 S1
IN0
Write Enable
OUT0
Multiplexer
Decoder
Writ
e co
ntro
l
12Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
Single port 4x2 Memory Array
De
Q De
Q De
QDe
Q
S0 S1
IN0
Write Enable
OUT0
De
Q De
Q De
QDe
QIN1
OUT1
Multiplexer bit[0]
Decoder
Writ
e co
ntro
lMultiplexer bit[1]
Critical paths
13
14Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
What is a critical path of scheme?
• Critical path is the slowest logic path in the circuit
• Reliable result of whole logic path can not be ready until critical path is passed by signal
15Intel Laboratory at Moscow Institute of Physics
and Technology MIPT-MIPS 2014 Project
Example of critical path finding:Multiplexer
Thank YouQ/A
16
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