5.1 Number Systems & Boolean Algebra

FE Electrical and Computer Exam Exam

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1 FE Electrical & Computer: Exam Map, Handbook & Strategy

1.1 Current Exam Facts 1.2 CBT Format & Scaled Scoring 1.3 The FE Reference Handbook 1.4 Approved Calculators & Test-Day Logistics 1.5 Study Plan & Time Strategy

2 Mathematics, Economics & Ethics

2.1 Algebra, Calculus & Differential Equations 2.2 Complex Numbers & Laplace Transforms 2.3 Probability & Statistics 2.4 Engineering Economics 2.5 Ethics & Professional Practice

3 Circuits, Electronics & Electromagnetics

3.1 DC Circuit Analysis 3.2 AC Steady-State & Phasors 3.3 Transient Response (RL, RC, RLC) 3.4 Electronics & Devices 3.5 Electromagnetics

4 Signals, Systems, Controls & Communications

4.1 Linear Systems & Transfer Functions 4.2 Signal Processing & Sampling 4.3 Control Systems 4.4 Communications

5 Digital Systems, Computers, Networks & Software

5.1 Number Systems & Boolean Algebra 5.2 Combinational & Sequential Logic 5.3 Computer Architecture & Microprocessors 5.4 Computer Networks 5.5 Software Engineering & Algorithms

6 Power, Materials & Final Readiness

6.1 Power Fundamentals & Three-Phase 6.2 Transformers & Rotating Machines 6.3 Power Electronics & Transmission 6.4 Properties of Electrical Materials & Engineering Sciences 6.5 Integrated Practice & Final Readiness

5.1 Number Systems & Boolean Algebra

Key Takeaways Explain This Topic AI

One hex digit equals exactly four binary bits, so 0xCA expands to 1100 1010 and equals 202 in decimal.

An n-bit two's complement system covers -2^(n-1) to +2^(n-1)-1, so 8 bits hold -128 to +127 with one extra negative value.

Negate a two's complement number by inverting every bit and adding 1; the same adder then does subtraction as addition.

De Morgan's theorems state NOT(A AND B) = NOT A OR NOT B and NOT(A OR B) = NOT A AND NOT B, making NAND and NOR universal gates.

A K-map group of 2^k adjacent 1-cells eliminates k variables, yielding a minimal sum-of-products expression.

Last updated: June 2026

Why number systems come first

The FE Electrical and Computer exam draws roughly 7 to 11 questions from Digital Systems , and most assume fluent base conversion. Computers store everything in binary (base 2), engineers read addresses in hexadecimal (base 16: digits 0-9 then A-F), sometimes group bits in octal (base 8), and people think in decimal (base 10). You must move between all four quickly: the NCEES FE Reference Handbook lists the place-value rules, but it cannot do the arithmetic for you.

The key shortcut is that one hex digit = four binary bits (because 2^4 = 16) and one octal digit = three binary bits (because 2^3 = 8). To convert hex to binary, expand each hex digit into its 4-bit pattern; to convert binary to hex, group bits in fours from the right. Decimal conversion uses positional weights: each binary position is a power of two, so 1011b = 8 + 0 + 2 + 1 = 11.

Base conversion reference

Memorize the first sixteen values so conversions become reflexive.

Decimal Binary (4-bit) Octal Hex
0 0000 0 0
5 0101 5 5
8 1000 10 8
10 1010 12 A
12 1100 14 C
15 1111 17 F

Worked conversion: Convert decimal 156 to binary and hex. Repeatedly divide by 2, reading remainders bottom-up: 156=10011100b. Group in fours from the right: 1001 1100 = 0x9C . Check: 9 16 + 12 = 144 + 12 = 156. To convert to octal, regroup the same bits in threes from the right: 010 011 100 = 0234 octal (2 64 + 3*8 + 4 = 156). Grouping bits is always faster and safer than dividing repeatedly by 8 or 16.