Spreadsheets, Structured Programming, and Flowcharts

FE Fundamentals of Engineering Exam

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1 Introduction to the FE Exam

About the FE Exam FE Exam Study Strategies Navigating the FE Reference Handbook

2 Mathematics (8–12 Questions)

Analytic Geometry and Trigonometry Single-Variable Calculus Differential Equations Linear Algebra and Matrix Operations Numerical Methods

3 Probability and Statistics (6–9 Questions)

Probability Fundamentals Probability Distributions Statistical Estimation and Hypothesis Testing

4 Chemistry (5–8 Questions)

Chemical Reactions and Stoichiometry Acids, Bases, and pH Oxidation-Reduction and Corrosion

5 Ethics and Professional Practice (5–8 Questions)

Engineering Ethics Fundamentals

6 Engineering Economics (6–9 Questions)

Time Value of Money Economic Analysis Methods

7 Statics (9–14 Questions)

Force Systems and Equilibrium Trusses, Frames, and Machines Centroids and Moments of Inertia Static Friction

8 Dynamics (9–14 Questions)

Particle Kinematics Kinetics: Force, Mass, and Acceleration Work, Energy, Impulse, and Momentum Rigid-Body Rotation and Mechanical Vibrations

9 Strength of Materials (9–14 Questions)

Stress and Strain Fundamentals Beam Analysis: Shear and Moment Diagrams Bending Stress and Torsion Stress Transformation and Material Failure

10 Materials Science (6–9 Questions)

Material Properties and Selection Phase Diagrams and Alloy Systems

11 Fluid Mechanics (12–18 Questions)

Fluid Properties and Statics Fluid Dynamics and Bernoulli's Equation Pumps, Turbines, and Flow Measurement

12 Thermodynamics and Heat Transfer (9–14 Questions)

Laws of Thermodynamics and Properties Thermodynamic Cycles and Applications Heat Transfer: Conduction, Convection, and Radiation

13 Basic Electrical Engineering (6–9 Questions)

Electrical Fundamentals and DC Circuits AC Circuits and Three-Phase Power

14 Safety, Health, and Environment (6–9 Questions)

Industrial Safety and Hazard Management

15 Instrumentation and Controls (4–6 Questions)

Sensors, Data Acquisition, and Control Systems

16 Computational Tools and Computer Science

Spreadsheets, Structured Programming, and Flowcharts

Key Takeaways Explain This Topic AI

Spreadsheet logic centers on cell references: relative (A1) shifts when copied, absolute ( $A$1 ) is locked, and mixed ( $A1 or A$1 ) locks one dimension — the #1 spreadsheet trap on the FE.

Structured programming uses three control structures — sequence, selection (if/else), and iteration (loops) — and any algorithm can be built from these without GOTO statements.

A flowchart's symbols are standardized: oval = start/end (terminator), rectangle = process, diamond = decision/branch, parallelogram = input/output, and arrows show flow direction.

Trace code or a flowchart by hand keeping a small table of variable values per pass; off-by-one errors and loop bounds (< vs ≤) are the most common FE distractors.

Logic diagrams combine Boolean operators AND, OR, NOT (and NAND/NOR/XOR); evaluate them or a truth table to predict an output from given inputs.

Last updated: June 2026

Spreadsheet Fundamentals

Spreadsheets organize data in a grid of cells named by column letter and row number (A1, B7). Formulas begin with = and combine cell references, operators ( + - * / ^ ), and built-in functions. The behavior that the FE tests most is how a reference changes when a formula is copied to another cell:

Reference style Example Behavior when copied
Relative A1 Both column and row shift by the copy offset
Absolute $A$1 Locked — never changes
Mixed (column locked) $A1 Column fixed, row shifts
Mixed (row locked) A$1 Row fixed, column shifts

If =A1*$B$1 in cell C1 is copied down to C2, it becomes =A2*$B$1 : the relative A1 advances to A2, while $B$1 stays put. This is the single most common spreadsheet question type. Common functions include SUM(range) , AVERAGE(range) , IF(test, value_if_true, value_if_false) , COUNT , MAX , and MIN . A range like A1:A10 denotes a contiguous block; SUM(A1:A10) adds all ten cells. Order of operations follows standard algebra (parentheses, then exponentiation, then multiply/divide, then add/subtract), so =2+3*4 returns 14, not 20.

Structured Programming and Control Flow

Structured programming builds any algorithm from just three control structures , with no jumps or GOTO statements:

Sequence — statements execute top to bottom, one after another.

Selection (branching) — IF / ELSE IF / ELSE chooses among paths based on a Boolean test.

Iteration (loops) — FOR (fixed count) and WHILE (condition-controlled) repeat a block.

The FE asks you to trace pseudocode and report the final value, not to write syntax. Keep a running table of each variable after every pass.

Worked Example — Loop Trace sum = 0
FOR i = 1 TO 4
sum = sum + i
END FOR

Pass-by-pass: i=1 → sum=1; i=2 → sum=3; i=3 → sum=6; i=4 → sum=10. Final sum = 10 .

Loop-bound trap: FOR i = 1 TO 4 runs four times (inclusive), but a condition WHILE i < 4 starting at i=1 and incrementing runs only while i is 1, 2, 3 — three times. Confusing < with ≤ is the classic off-by-one error. Watch also for variables modified inside a loop and for nested loops, where the inner loop completes fully on each outer pass (an outer loop of 3 around an inner loop of 4 executes the inner body 12 times).

Flowcharts and Logic Diagrams

A flowchart depicts an algorithm with standardized symbols. Knowing the shapes lets you read or assemble one on the exam:

Symbol Meaning
Oval (terminator) Start or End
Rectangle Process / computation step
Diamond Decision (yes/no branch)
Parallelogram Input or Output
Arrow Direction of flow

A diamond always has one entry and two exits (true/false), which is how loops and branches are drawn. To trace a flowchart, start at the oval and follow arrows, evaluating each diamond against the current variable values exactly as you would trace code.

Boolean Logic and Logic Diagrams

Digital and control problems use Boolean logic with operators AND (true only if all inputs true), OR (true if any input true), and NOT (inverts). NAND, NOR, and XOR are derived. A truth table lists the output for every input combination:

A B A AND B A OR B A XOR B
0 0 0 0 0
0 1 0 1 1
1 0 0 1 1
1 1 1 1 0

XOR (exclusive OR) is true only when inputs differ — a frequent distractor against OR. The NCEES outline lists logic diagrams under Instrumentation and Controls, where they describe control interlocks: evaluate the gates from inputs toward the output to find whether an alarm or shutoff activates. Expect one or two questions asking you to read a small gate network or complete a truth-table row.

Data Representation and Algorithm Basics

Computers store everything in binary (base 2). Each bit is 0 or 1; eight bits make a byte. To convert binary to decimal, sum the place values: 1011₂ = 8 + 0 + 2 + 1 = 11₁₀. To convert decimal to binary, repeatedly divide by 2 and read the remainders bottom-up.

Hexadecimal (base 16) compresses binary four bits at a time (0–F), so it appears in addresses and color codes. Programs also distinguish data types — integers (whole numbers), floating-point (reals, with finite precision that causes round-off), Boolean (true/false), and strings (text) — and using the wrong type is a real source of bugs, e.g., integer division 7/2 yielding 3 rather than 3.5.

Concept Key fact
Bit / byte 1 byte = 8 bits = 256 distinct values
Binary→decimal Sum place values (…8 4 2 1)
Floating point Finite precision → round-off error
Integer division Truncates the fractional part
Connecting Tools to Numerical Methods

Spreadsheets and short programs are how engineers actually execute the numerical methods from the Mathematics outline: iterating the Newton-Raphson formula in successive cells until the change falls below a tolerance, or summing a trapezoidal-rule series down a column.

Convergence means each iterate gets closer to the answer; a well-built loop stops when |xₙ₊₁ − xₙ| < ε rather than after a fixed count. Recognize that round-off (from finite floating-point precision) and truncation (from stopping a series early) both limit accuracy, and that a sensible algorithm trades iterations for precision. On the FE, this links the computational-tools questions back to roots-of-equations and approximation topics — the tool is the spreadsheet or loop, but the underlying method is the math you already know.