Tech Logic

Module 2.5: Tech Logic

Why Tech Logic Matters on the STEM Assessment

The STEM Thinking Skills Assessment isn't just about math and science knowledge --- it tests how you think. A significant portion of the test involves what we call "tech logic": the ability to follow logical sequences, interpret processes, recognize patterns, and apply systematic reasoning.

You don't need to be a programmer or a computer scientist to do well on these questions. But you do need to understand how logical systems work. This module teaches you the foundational concepts --- Boolean logic, flowcharts, conditional reasoning, input/output patterns, and circuit logic --- and gives you practice applying them to the kinds of problems you'll encounter on test day.

Boolean Logic and Truth Tables

Boolean logic is the foundation of how computers think, but it's also the foundation of how clear thinkers reason through problems. There are only two values in Boolean logic: TRUE and FALSE. Everything else is built from three basic operations.

AND --- Both conditions must be true for the result to be true.

Think of it this way: "I'll go to the movies if I finish my homework AND my mom says yes." Both things have to happen. If you finish your homework but your mom says no, you're not going. If your mom says yes but you didn't finish your homework, still not going. You only go if both conditions are met.

• TRUE AND TRUE = TRUE

• TRUE AND FALSE = FALSE

• FALSE AND TRUE = FALSE

• FALSE AND FALSE = FALSE

OR --- At least one condition must be true for the result to be true.

"I'll be happy if we get pizza OR tacos for dinner." You're happy with pizza. You're happy with tacos. You're happy with both. The only way you're not happy is if you get neither.

• TRUE OR TRUE = TRUE

• TRUE OR FALSE = TRUE

• FALSE OR TRUE = TRUE

• FALSE OR FALSE = FALSE

NOT --- This flips the value. NOT TRUE becomes FALSE. NOT FALSE becomes TRUE.

"The store is NOT open" means it's closed. Simple reversal.

• NOT TRUE = FALSE

• NOT FALSE = TRUE

Combining Operations

Here's where it gets interesting. Real problems combine these operations:

"You can join the robotics team if you have a B average AND (you're in 8th grade OR you have teacher approval)."

Let's say a student has an A average (TRUE for the B-average requirement), is in 7th grade (FALSE for 8th grade), and has teacher approval (TRUE).

Work from the inside out:

1. 8th grade OR teacher approval = FALSE OR TRUE = TRUE

2. B average AND (result from step 1) = TRUE AND TRUE = TRUE

The student can join. Now try the same student without teacher approval:

1. FALSE OR FALSE = FALSE

2. TRUE AND FALSE = FALSE

Not eligible.

Practice: Truth Tables

A truth table lists every possible combination of inputs and shows the output for each. Here's one for the expression: A AND (B OR C)

When A is TRUE, B is TRUE, C is TRUE: B OR C = TRUE, so A AND TRUE = TRUE

When A is TRUE, B is TRUE, C is FALSE: B OR C = TRUE, so A AND TRUE = TRUE

When A is TRUE, B is FALSE, C is TRUE: B OR C = TRUE, so A AND TRUE = TRUE

When A is TRUE, B is FALSE, C is FALSE: B OR C = FALSE, so A AND FALSE = FALSE

When A is FALSE, B is TRUE, C is TRUE: A AND anything = FALSE

When A is FALSE, B is TRUE, C is FALSE: FALSE

When A is FALSE, B is FALSE, C is TRUE: FALSE

When A is FALSE, B is FALSE, C is FALSE: FALSE

The key insight: when you see AND, you know the result is only TRUE when everything involved is TRUE. When you see OR, the result is FALSE only when everything involved is FALSE.

Flowchart Interpretation and Process Sequencing

Flowcharts are visual representations of processes. On the STEM assessment, you might be given a flowchart and asked what output it produces, where a process ends up, or what step comes next.

The Basic Shapes

• Ovals (rounded rectangles) represent START and END points

• Rectangles represent actions or processes --- something happens here

• Diamonds represent decisions --- yes/no questions that send you in different directions

• Arrows show the flow direction

How to Read a Flowchart

Always start at the START oval and follow the arrows. When you hit a diamond, evaluate the condition and follow the correct path (usually labeled Yes/No or True/False). Keep going until you reach an END oval or the final output.

Example Flowchart Scenario

Imagine a flowchart for deciding what to wear:

START → Is it raining? → (Yes) → Wear a raincoat → Is it cold? → (Yes) → Add a sweater underneath → END

→ (No) → Is it cold? → (Yes) → Wear a jacket → END

→ (No) → Wear a t-shirt → END

If the weather is rainy and warm, you'd trace: START → Is it raining? → Yes → Wear a raincoat → Is it cold? → No → END. Your outfit: raincoat, no sweater.

Process Sequencing

Sometimes the test gives you a set of steps out of order and asks you to arrange them logically. The trick is to identify:

1. What must happen first (what has no prerequisites)?

2. What depends on something else being done?

3. What's the final output or result?

Example: Put these steps in order for making a scientific measurement:

• Record the result in your data table

• Calibrate the instrument

• Take the measurement

• Check that the measurement seems reasonable

• Select the appropriate instrument

Logical order: Select the appropriate instrument → Calibrate the instrument → Take the measurement → Check that the measurement seems reasonable → Record the result in your data table

You can't calibrate an instrument you haven't selected yet. You can't check a measurement you haven't taken. The dependencies reveal the sequence.

Basic Programming Logic

You don't need to know any programming language for the STEM assessment. But you do need to understand the logical structures that all programs are built from. Think of these as patterns of reasoning, not code.

If/Then (Conditional Reasoning)

An if/then statement is just a rule: IF some condition is true, THEN do something.

"If the temperature is above 90 degrees, then turn on the air conditioning."

This only triggers when the condition is met. If it's 85 degrees, nothing happens. If it's 95 degrees, the AC turns on.

If/Then/Else

This adds an alternative: IF the condition is true, do one thing. ELSE (otherwise), do something different.

"If the temperature is above 90, turn on the AC. Otherwise, open the windows."

Now something happens regardless. Above 90? AC. At or below 90? Windows.

Nested Conditions

Conditions inside conditions:

"If it's a weekday, then: if school is in session, then go to school; otherwise, sleep in. If it's a weekend, then go play."

This creates a decision tree. First you check: weekday or weekend? Then, if weekday, you check another condition.

Loops

A loop repeats an action until a condition is met.

"Keep stirring the soup until it boils."

The action (stirring) repeats. Each time through the loop, you check the condition (is it boiling?). When the condition is finally true, the loop stops.

"For each student in the class, check if they turned in their homework."

This loop goes through a list --- every student --- and performs the same check on each one. When you've gone through all students, the loop ends.

Practice Scenario

A vending machine follows this logic:

1. Accept coins and keep a running total

2. If the total is less than the price, go back to step 1

3. If the total equals or exceeds the price, dispense the item

4. If the total exceeds the price, calculate change

5. If change is owed, dispense change

6. Return to ready state

Question: A drink costs $1.50. You insert a quarter, then a dollar coin, then another quarter. What happens at each step?

After quarter: Total = $0.25. Less than$1.50 → accept more coins

After dollar: Total = $1.25. Less than$1.50 → accept more coins

After second quarter: Total = $1.50. Equals$1.50 → dispense drink. $1.50 -$1.50 = $0.00 change. No change to dispense. Return to ready.

Input/Output Pattern Identification

These questions give you a set of inputs and outputs and ask you to figure out the rule, then predict what output a new input would produce.

Example 1: Simple Numeric Pattern

Input → Output

2 → 5

4 → 9

7 → 15

10 → 21

What's the rule? Look at the relationship between each input and output:

• 2 → 5: difference is 3, or 2 × 2 + 1 = 5

• 4 → 9: difference is 5, or 4 × 2 + 1 = 9

• 7 → 15: difference is 8, or 7 × 2 + 1 = 15

• 10 → 21: difference is 11, or 10 × 2 + 1 = 21

The rule is: multiply the input by 2, then add 1.

So if the input is 13, the output is 13 × 2 + 1 = 27.

Example 2: Two-Input Function

Input A, Input B → Output

3, 2 → 8

5, 1 → 11

4, 3 → 11

2, 5 → 9

Test different operations:

• 3 + 2 = 5 (not 8)

• 3 × 2 = 6 (not 8)

• 3 × 2 + 2 = 8 ✓ ... but check: 5 × 1 + 2 = 7, not 11

• 3 + 2 × 2 + 1 = 8? That's 3 + 4 + 1 = 8 ✓ ... but 5 + 1 × 2 + 1 = 8, not 11

• 2 × 3 + 2 = 8 ✓, 2 × 5 + 1 = 11 ✓, 2 × 4 + 3 = 11 ✓, 2 × 2 + 5 = 9 ✓

The rule is: 2 × A + B.

Strategy for Finding Patterns

1. Start with the simplest operations: addition, subtraction, multiplication

2. Check if a rule works for ALL given pairs, not just one

3. If simple operations don't work, try combinations (multiply then add, square then subtract)

4. Look for the relationship between the input and output, not just the output values themselves

Example 3: Letter/Symbol Transformation

Input → Output

ABC → CBA

HELLO → OLLEH

STEM → METS

The rule: the output is the input reversed.

What would LOGIC become? CIGOL.

Not all patterns are numeric. Stay alert for reversals, letter shifts, positional changes, and other transformations.

Circuit and Systems Logic

On the STEM assessment, you might see questions about how systems work --- not complex electrical engineering, but basic logic about how components interact.

Series vs. Parallel

In a series system, components are connected one after another. If any single component fails, the whole system fails. Think of old-fashioned Christmas lights: one bulb burns out, the whole string goes dark.

In a parallel system, components operate independently. If one fails, the others keep working. Think of the lights in your house: the kitchen light burning out doesn't affect the living room light.

Logic Gates (Conceptual)

Logic gates are physical implementations of Boolean logic. You already know the logic --- now imagine each operation as a physical gate that electricity flows through.

An AND gate only lets a signal through if both inputs are on. Think of it as two switches in series --- both must be flipped for the light to work.

An OR gate lets a signal through if either input is on. Think of it as two switches in parallel --- either one can turn on the light.

A NOT gate (inverter) flips the signal. If the input is on, the output is off, and vice versa. Think of it as a switch that works backwards.

System Logic Example

A security system has three sensors: a door sensor (D), a window sensor (W), and a motion detector (M). The alarm triggers if: (D OR W) AND M.

Translation: The alarm goes off if the motion detector is triggered AND either the door or window sensor is triggered.

Scenario 1: Door opens (D = TRUE), windows closed (W = FALSE), motion detected (M = TRUE).

(TRUE OR FALSE) AND TRUE = TRUE AND TRUE = TRUE → Alarm sounds.

Scenario 2: Door closed (D = FALSE), windows closed (W = FALSE), motion detected (M = TRUE).

(FALSE OR FALSE) AND TRUE = FALSE AND TRUE = FALSE → No alarm. (Motion alone isn't enough --- a sensor must also trigger.)

Scenario 3: Door opens (D = TRUE), windows closed (W = FALSE), no motion (M = FALSE).

(TRUE OR FALSE) AND FALSE = TRUE AND FALSE = FALSE → No alarm. (The door opened but no motion was detected --- maybe the wind blew it open.)

Practice Scenarios

Scenario 1: Boolean Logic

A school club has these membership rules: You must be in grade 7 OR grade 8, AND you must have a GPA of 3.0 or higher, AND you must NOT have any disciplinary referrals.

Determine eligibility for each student:

• Student A: Grade 8, GPA 3.5, no referrals

• Student B: Grade 6, GPA 3.8, no referrals

• Student C: Grade 7, GPA 2.9, no referrals

• Student D: Grade 8, GPA 3.2, one referral

Answers:

• Student A: (TRUE) AND (TRUE) AND (NOT FALSE = TRUE) → TRUE. Eligible.

• Student B: (FALSE) AND (TRUE) AND (TRUE) → FALSE. Not eligible (wrong grade).

• Student C: (TRUE) AND (FALSE) AND (TRUE) → FALSE. Not eligible (GPA too low).

• Student D: (TRUE) AND (TRUE) AND (NOT TRUE = FALSE) → FALSE. Not eligible (has a referral).

Scenario 2: Flowchart Logic

A library's late book process works like this: When a book is returned, check if it's overdue. If not overdue, shelve it. If overdue, check if it's more than 30 days late. If 30 days or fewer, charge a fine of $0.25 per day. If more than 30 days, charge a flat$10 fee and send a warning letter. After any fine is charged, shelve the book.

A book was due January 10 and returned January 28. What happens?

The book is 18 days overdue (overdue = YES). Is it more than 30 days late? No (18 ≤ 30). Charge $0.25 × 18 =$4.50 fine. Shelve the book.

Scenario 3: Input/Output

Find the rule and predict the missing output:

Input → Output

1 → 1

2 → 4

3 → 9

4 → 16

5 → ?

The outputs are 1, 4, 9, 16 --- perfect squares. The rule is: input × input (or input squared). So 5 → 25.

Now try this one:

Input → Output

1 → 2

2 → 6

3 → 12

4 → 20

5 → ?

Differences between outputs: 4, 6, 8 --- increasing by 2 each time. Next difference would be 10, so 20 + 10 = 30.

Or look for a formula: 1×2 = 2, 2×3 = 6, 3×4 = 12, 4×5 = 20, 5×6 = 30. The rule is: input × (input + 1).

Scenario 4: System Logic

A smart thermostat follows these rules:

• If the temperature is below 68°F AND someone is home, turn on the heater

• If the temperature is above 76°F AND someone is home, turn on the AC

• If nobody is home, turn everything off regardless of temperature

• If the temperature is between 68°F and 76°F, do nothing

It's 65°F and nobody is home. What does the thermostat do?

Even though the temperature is below 68°F, the "nobody is home" rule kicks in: turn everything off. The AND condition for the heater requires someone to be home, which is FALSE, so the heater stays off.

Scenario 5: Process Sequencing

A student is building a simple robot. Put these steps in the most logical order:

• Test the robot's movements

• Write the control program

• Assemble the frame and wheels

• Debug any errors in the program

• Design the robot on paper

• Connect the motors and sensors

• Gather materials and components

Logical order: Design the robot on paper → Gather materials and components → Assemble the frame and wheels → Connect the motors and sensors → Write the control program → Test the robot's movements → Debug any errors in the program

You need a design before gathering materials, a frame before connecting motors, a program before testing, and testing before debugging.

Key Takeaways for Test Day

• When you see a Boolean logic problem, break it into individual TRUE/FALSE values first, then combine them step by step using AND, OR, and NOT rules.

• For flowcharts, trace the path with your finger (or in your mind). Don't skip steps or assume you know where it goes --- follow every arrow and evaluate every decision.

• For input/output patterns, always verify your rule against ALL given examples, not just the first one.

• For process sequencing, identify dependencies --- what must happen before what?

• These questions reward careful, systematic thinking. Rushing leads to careless errors. Slow down, trace through the logic, and trust the process.