7.3 Computer Fundamentals, Programming & Data Logic

7.3 Computer Fundamentals, Programming & Data Logic

Computer Fundamentals and Computer Programming constitute a dedicated portion of the ESAS subject area in the REE Licensure Examination. Electrical engineers regularly interface with microcontrollers, PLCs, embedded control systems, digital signal processors, and software algorithms.

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1. Computer Hardware & Systems Architecture

The Von Neumann Architecture

Most modern computing systems are based on the Von Neumann Architecture, which features stored programs where instructions and data share the same memory space.

                  VON NEUMANN SYSTEM ARCHITECTURE
  ┌─────────────────────────────────────────────────────────────┐
  │                 CENTRAL PROCESSING UNIT (CPU)               │
  │  ┌─────────────────────────┐   ┌─────────────────────────┐  │
  │  │ Arithmetic Logic Unit   │   │      Control Unit       │  │
  │  │        (ALU)            │   │          (CU)           │  │
  │  └────────────┬────────────┘   └────────────┬────────────┘  │
  │               │    ┌───────────────────┐    │               │
  │               └───►│ CPU Registers (PC,│◄───┘               │
  │                    │ IR, MAR, MDR, ACC)│                    │
  │                    └───────────────────┘                    │
  └──────────────────────────────┬──────────────────────────────┘
                                 │ System Bus (Data, Address, Control)
  ┌──────────────────────────────┴──────────────────────────────┐
  │                     MAIN MEMORY (RAM / ROM)                 │
  └──────────────────────────────┬──────────────────────────────┘
                                 │ I/O Bus
  ┌──────────────────────────────┴──────────────────────────────┐
  │                 INPUT / OUTPUT (I/O) DEVICES                │
  └─────────────────────────────────────────────────────────────┘

Key CPU Components & Memory Hierarchy

• Arithmetic Logic Unit (ALU): Performs integer arithmetic (add, subtract) and bitwise logical operations (AND, OR, XOR, shift).
• Control Unit (CU): Fetches instructions from memory, decodes operation codes, and generates timing signals.
• Registers: High-speed storage inside CPU (e.g., Program Counter PC, Instruction Register IR, Accumulator ACC).
• Memory Hierarchy: Registers (Fastest/Smallest) $\rightarrow$ L1/L2/L3 Cache $\rightarrow$ Main Memory (RAM) $\rightarrow$ Secondary Storage (NVMe/SSD/HDD) (Slowest/Largest).

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2. Number Systems & Data Representation

Positional Radix Systems

2's Complement Signed Integer Representation

To represent negative integers in binary using $n$ bits:

1. Write the $n$-bit magnitude binary representation of the positive number.
2. Invert all bits ($0 \rightarrow 1$ and $1 \rightarrow 0$) to form the 1's complement.
3. Add 1 to the 1's complement to yield the 2's complement.

• Representable Range for $n$ bits: $-2^{n-1} \le X \le 2^{n-1} - 1$
  • For 8 bits ($n=8$): Range is $-128$ to $+127$.
  • For 16 bits ($n=16$): Range is $-32,768$ to $+32,767$.

IEEE 754 Floating-Point Standard (Single Precision 32-bit)

$\text{Value} = (-1)^S \times 1.M \times 2^{E - 127}$

• Sign Bit ($S$): Bit 31 (1 bit, 0 = Positive, 1 = Negative)
• Biased Exponent ($E$): Bits 30–23 (8 bits, Bias = 127)
• Mantissa / Significand ($M$): Bits 22–0 (23 bits, implicit leading 1)

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3. Boolean Algebra & Logic Gates

Digital logic circuits implement Boolean functions using basic and universal logic gates.

Basic Logic Gate Summary

Key Boolean Algebra Laws

• De Morgan's First Law: $\overline{A + B} = \bar{A} \cdot \bar{B}$
• De Morgan's Second Law: $\overline{A \cdot B} = \bar{A} + \bar{B}$
• Absorption Law: $A + (A \cdot B) = A \quad \text{and} \quad A \cdot (A + B) = A$
• Consensus Theorem: $A B + \bar{A} C + B C = A B + \bar{A} C$

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4. Structured Programming & Algorithm Logic

Control Flow Structures

High-level languages (such as C, C++, Python) structure execution logic into three fundamental patterns:

1. Sequence: Step-by-step execution of linear statements.
2. Selection (Branching): Decision-making via if-else or switch-case statements based on conditional boolean evaluation.
3. Iteration (Looping): Repeating code blocks via for, while, or do-while constructs.

OSI 7-Layer Networking Reference Model

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Solved Practice Examples

Example 1: 2's Complement Conversion

Problem: Find the 8-bit 2's complement binary representation of the decimal integer $-43_{10}$.

Solution:

1. Write positive magnitude $+43_{10}$ in 8-bit binary: $+43_{10} = 00101011_2$
2. Take the 1's complement (invert all bits): $\text{1's Comp} = 11010100_2$
3. Add 1 to obtain 2's complement: $\text{2's Comp} = 11010100_2 + 1_2 = 11010101_2$ Thus, $-43_{10} = 11010101_2$.

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Example 2: Boolean Expression Simplification

Problem: Simplify the Boolean expression $Y = A B C + A B \bar{C} + A \bar{B} C$.

Solution:

1. Factor out $AB$ from the first two terms: $Y = A B (C + \bar{C}) + A \bar{B} C$
2. Apply inverse law $C + \bar{C} = 1$: $Y = A B (1) + A \bar{B} C = A B + A \bar{B} C$
3. Factor out $A$ from remaining terms: $Y = A (B + \bar{B} C)$
4. Apply distributive law $B + \bar{B} C = (B + \bar{B})(B + C) = 1 \cdot (B + C)$: $Y = A (B + C) = A B + A C$