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Title

Description


Numbers (Existence)

Numbers do not exist in the computer. We
make a mental mapping between the physics of the computer
(voltage levels, etc.) and the mathematics in our head.


Number Systems. Ways to represent numbers

Why the decimal system (base 10) is nothing
special. Base6 is better, but the numbers get large.
Base20 is often used (Mayans) as well as Babylonian
(base60). Romans were strange. Binary is great for
computing because the underlying electronics are binary.


Number Conversions

How to convert numbers from any number base
to any other number base.


Negative Numbers

How are negative numbers stored in the
computer? We will look here at three conventions:
Signmagnitude, 1scomplement and 2'scomplement. We will
see that 2'scomplement is good because subtractions can
then be done by adding the negative numbers.


Boolean Algebra

The underlying mathematics of a computer.
Boolean Algebra, that itself is based on Set Theory. The
Huntington Postulates are presented that will form our
basis. Some important relations are given.


de Morgan's Laws

The de Morgan's Law tell us that the
negation of a 'sum' (OR) is the 'product' (AND) of
negations, NOS=PON and the negation of a 'product' (AND)
is the 'sum' (OR) of negations, NOP=SON.
These rules will come in very handy in the future when we
design digital circuits.


Truth Tables

Truth Tables are a way to summarize the
behavior of a logic circuit. They specify the output value
(0 or 1) for all combinations of input values at the gate.
In total there are 2^4 = 32 possible twoinputoneoutput
gates. The most basic ones are: AND, OR, NAND, NOR, NOT
and XOR.


Sum of Products
Product of Sums

How to implement any logic function with
only AND, OR and NOT operations.


Karnaugh Maps

Karnaugh Maps are an easy way to simplify
the expressions found by the SOP (sum of products) and POS
(product of sums) methods


Karnaugh Maps 2

An additional look at Karnaugh Maps. How
does the XOR operation look in a KM. And how do we deal
with 'don't cares'?


Electronics, CMOS

How are the basic gates implemented in
electronics? We take a look at the NOT, NAND, NOR, AND, OR
and XOR gates implemented in CMOS (complementary metal
oxide semiconductor) technology.


Multiplexer 
A real life example how to build a useful
digital electronic circuit on basis of a functional
description. A multiplexer (one of the inputs is copied to
the output, determined by the selector lines) 

Memory (latch & flipflop)

When feedback is used in logic circuits,
the emergent property can be that the circuit has memory;
the output no longer only depends on the input, but also
on the current state. 

Master/Slave Flipflops

A masterslave flipflop is made of two
gated S/R latched placed in series. At the first halve of
a clock cycle the master is processing the signal, while
at the second halve the slave is processing.


Master/Slave Flipflops 2

A close look at an edgetriggered
masterslave Dtype flipflop.


Finite State Machines

A finite state machine has both a logic
array and memory. Four types exist: 1) Mealy Machines
(input, output and memory), 2) Moore Machines (sequencers)
with output and memory but no input, 3) Boole Machines
with input and output but no memory, and 4) Berkeley
Machines with input and memory but no output. An example
is given of a Moore Machine sequencer, a 3bit counter
based on Ttype flipflop memory elements.


Finite State Machines 2. S/R counter

Another look at a Moore Machine (Finite
State Machine with no input). In this case an example of
how to build a 2bit counter with S/R flipflops


FSM Mealy machine. Parity checker

We will take a look at a full Mealy machine
(with input and output), namely a parity checker. First we
design a state diagram: a circle for all states and draw
arrows how the states can change with input. Then we
decide for our hardware (how many and what type of
flipflops to use for the state and output). And then we
can implement the things just as we had done for a
(noninput) Moore machine. An action table. An excitation
table. The logic array via Karnaugh maps, etc.


FSM, Edge Detector

Here we take a look at another full Finite
State Machine (Mealy Machine) with input and output and
memory, namely an edge detector.
