# 6.1.1 Binary Numbers (Short Circuit Video)

Description: A review of how counting works with normal (base 10) numbers. Then it is relate to the new concept of binary numbers; a system which is implemented in computers to represent numbers.

Script:

First Let's look at how we're used to counting.

We have 10 digits in our number system - 0 through 9.

There's no number bigger than 9 that we can fit in the 1's place. Or any place for that matter.

Suppose we have the number 327.

7 in the ones place

2 in the tens place

and 3 in the hundreds place.

Now let's count up from here.

328

329

Hmm, we can't fit any more value in the 1's place so we have to "carry over" - Like this.

This system can't be directly transferred to digital circuits, since we can only do true or false comparisons. On or off, 1 or 0.

But even with that, we still have two digits to work with.

Let's explore this system by counting upwards using the same carry over rules as before.

1

Now we can't fit any more value into this place, so we have to carry over.

And set this place to 0.

The value shown here is 2, so we can conclude that this is the 2's place.

3

Now we're faced with a carry again.

It can't hold any more value so we have to carry again.

set the 2's place to 0.

and set the 1's place to zero.

We know this number is 4, so this must be the 4's place.

We can continue this trend onward

5

6

7

The system that we are exploring is called binary, and each place is called a "bit"

This is a 3 bit number

Binary enables us to execute highly accurate and repeatable arithmetic and comparison using digital logic circuits.

Using what we learned -- see if you can try and count up to the number 12 using binary.

That's it for today's Short Circuit. Thanks you for Watching!

# 6.2 Power Electronics

Any articles concerning power electronics

# 6.2.1 DC-DC Voltage Converters

Articles discussing the process of converting DC to another level of DC

# 6.2.1.1 Boost Converter - Component Calculator

## Input Parameters

 VSAT Saturation voltage of the output transistor VF Forward voltage drop of the diode VIN Typical input voltage VMIN The minimum voltage of the input VOUT Desired output voltage IOUT Desired output current fMIN Minimum desired output switching frequency VRIP Desired peak to peak output ripple voltage R1 Resistor for setting VOUT

## Calculated Component Values

 R1 Resistor for setting VOUT R2 Resistor for setting VOUT R3 Switch Biasing (constant) RPD Pull down resistor for transistor (constant) RSC Current sense resistor CT Timing capacitor CO Output capacitor LMIN Minimum inductance for output

# 6.2.1.2 Buck Converter - Component Calculator

## Input Parameters

 VSAT Saturation voltage of the output transistor VF Forward voltage drop of the diode VIN Typical input voltage VMIN The minimum voltage of the input VOUT Desired output voltage IOUT Desired output current fMIN Minimum desired output switching frequency VRIP Desired peak to peak output ripple voltage R1 Resistor for setting VOUT

## Calculated Component Values

 R1 Resistor for setting VOUT R2 Resistor for setting VOUT RPD Pull down resistor for transistor (constant) RSC Current sense resistor CT Timing capacitor CO Output capacitor LMIN Minimum inductance for output

# 6.2.1.3 Low Drop Out Regulators vs. Buck Converters

In this video the energy efficiencies of Low Drop Out (LDO) regulators and Buck converters is discussed. A quick graph is generated in Sage Mathematics to compare the two circuits power consumption

LDO Efficiency:

$$P_{loss}=I*(V_{in}-V_{out})$$

Where $P_{loss}$ is heat dissipation, $I$ is the current drawn on the output, $V_{in}$ is the input voltage, and $V_{out}$ is the output voltage.

Buck Efficiency:

$$P_{loss}=(1-E)*V_{out}*I$$

Where $P_{loss}$ is heat dissipation, $E$ is the calculated efficiency, $I$ is the current drawn on the output, and $V_{out}$ is the output voltage.

Sage Simulation Script:

var("Vin",latex_name="V_{in}")
var("Vout",latex_name="V_{out}")
var("I")
var("E")
Vin=17
Vout=12
E=.87
PlossLDO=I*(Vin-Vout)
PlossBuck=Vout*I*(1-E)
plot(PlossLDO,(I,0,1.5))+plot(PlossBuck,(1,0,1.5),color="red")

References:

# 6.3.1 Axioms of Probability

• Axiom I: The probability of an event happening positive, or zero. $P[A]\leq0$
• Axiom II: The total (added) probability of each event in a set is equal to one. $P[S]=1$
• Axiom III: If two subsets have no elements in common, then the probability of the two sets combined into one set is the individual probability of the individual sets added together. $\text{If } A\cap{B}= \emptyset\text{ then } P[A\cup{B}] = P[A]+P[B]$

# 6.3.2 Terms & Definitions

• Compliment: $S^c$ takes the exact opposite of the set it's acting on. A complimented compliment makes no compliment at all.
• DeMorgan's Rule: An equivalent statement of set operators can be found by complimenting each set, flipping the operators, and complimenting the final output.
• Intersection Operator: The intersection operator $\cap$, finds only the elements in common between two sets. This is the same as the logical AND function
• Sample Space: The sample space, denoted as $S$ is a set of all possible outcomes of an event. It can either be a list, like $S=\{ 1,2,4,8\}$, or a property, or list or properties that defines and fully constrains a variable. An example of the latter is $S=\{ x:x \text{ is even and } 0\leq{x}\leq{10}\}$ or $S=\{ (x,y): x+y=1, 0\leq{x}\leq{1},0\leq{y}\leq{1}\}$
• Union Operator: The union operator, $\cup$, combines to sets together - but keep in mind it does not repeat elements which are common between the two sets. This is the same as a logical OR function.