Asynchronous Sequential Circuits
A type of circuit without clocks (therefore NO flip-flops), but with the concept of
memory.
The concept of memory is obtained through the use of: latches and/or circuit
delay and combinational loops.
Asynchronous sequenti

VHDL process statements
Recall that concurrent signal assignment statements all operate in parallel.
The VHDL process statement is effectively a block around a bunch of logic and
control.
Inside of a process statement, statements are executed sequentiall

Algorithmic state machines (ASM)
An alternative to a state diagram which is sometimes nicer when our hardware is
implementing an algorithm that can be drawn as a flowchart.
The ASM is tied closely with a hardware implementation.
The ASM consists of three

State assignment
Given a state table or state diagram with symbolic states, we need to assign binary
patterns to the states.
Since both circuit outputs and flip-flop input equations depend on current state,
the complexity of the output and flip-flop inpu

Synchronous circuit analysis
Given a circuit (containing combinational logic and flip-flops), synchronous circuit
analysis involves figuring out what the circuit is doing.
i.e., How does the circuit transition from state to state as clock edges arrive?
W

Impact of flip-flop type on sequential circuit design
Flip-flops hold the current state information and the next state information is
determined by the flip-flop input equations.
When designing a synchronous circuit, using DFF is an obvious choice because

Clocked (synchronous) sequential circuits
Synchronous sequential circuits have the concept of memory and use a clock to
determine when things happen in a circuit.
inputs
combinatorial
circuit
outputs
next state
function flip-flops
current
state
clock
Whe

Sequential circuits
Circuits with simple logic gates are known as combinational circuits. These are the
types of circuits we have talked about up to this point in the course.
We can include storage elements into a circuit that act like memory and store a

Other types of concurrent VHDL signal assignments
The <= operator is not the only means by which we can perform combinational
assignments in VHDL.
There are other concurrent signal assignment operators that make writing VHDL a bit
easier.
ECE124 Digital C

Registers
A single FF stores one bit A group of n FFs
stores n-bits and is called an n-bit register.
Illustration:
When clear=0, all flip-flop outputs are forced
to zero (active low reset).
When clear=1, the rising edge of the clock
(the active clock e

What Is VHDL (IEEE Standard 1076)?
VHDL is an acronym that stands for VHSIC Hardware Description Language.
The acronym VHSIC in turn stands for Very-High Speed Integrated Circuit program.
Program sponsored by US Department of Defense (DOD) with the goal o

Component instantiations
Often we will have a VHDL Description of part of a circuit that we would like to use inside of
another circuit.
As an example, consider building an n-bit ripple adder from 1-bit full adders.
We can use VHDL descriptions inside of

Combinational circuits (other useful combinational blocks)
Many types of useful combinational circuits such as comparators, encoders
and decoders, multiplexers and demultiplexers, and so on.
We should be familiar with such blocks since they occur so often

Combinatorial circuits (arithmetic)
Some combinational circuits are very comment and it is worth looking at
them in more detail.
One particular class of very useful circuits are arithmetic circuits; i.e., those
circuits used for performing operations su

Factoring (and multi-level implementations)
Sometimes 2-level implementations can just be large; i.e., even with simplification,
we still end up with large gates and many of them.
Sometimes, the solution is to factor an equation to see if there are simple

Introduction
Digital circuits and systems are essentially a means to perform computation
and logical operations via machines.
It turns out that machines to perform computation and logic operations deal
best when working with only binary values; i.e., on

Number representations
We often want to do numerical computations in digital systems so we need to
understand how to represent and manipulate binary numbers (and, in general, in
number systems other than decimal).
ECE124 Digital Circuits and Systems
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Logic Minimization with Karnaugh Maps (KMaps)
Boolean algebra can be used to find minimal SOP (POS) logic equations, but it
is hard to automate and not very systematic.
For small logic functions (<=5 inputs), we can use Karnaugh Map (KMap).
KMaps allow

NAND/NOR Only Implementations
Although we can implement any circuit with AND/OR/NOT, we can also implement
any circuit with only NAND or NOR gates.
We might want to do this because of technology considerations; That is, these gates
might be cheaper to imp

Combinational circuits
A combinatorial circuit is one that consists of logic gates with outputs that are
determined entirely by the present value of the inputs.
Combinatorial circuits might be 2-level logic (SOP,POS) or multi-level.
Black box illustration

XOR gates
XOR gates are expensive to implement in silicon, but they are very useful for circuits like
parity checkers and arithmetic circuits (e.g., adders, subtractors, and so forth).
Sometimes, we can find an XOR gate hidden or buried inside of a lot of