Intro to Computer Organization, Number & Data Representation

Define a computer as a machine that can do work by carrying out instructions. Explain how it stores and processes data in binary according to a variable program.

Explore the basic organization of a simple computer, including cpu, main memory, i/o devices, system bus; understand the control unit, alu, and register file with special and general registers.

Explain how a program provides instructions to a computer via ordered machine instructions derived from high-level languages, executed sequentially by the CPU, with jumps, arithmetic, load/store, and input/output operations.

We bridge the gap between human language and machine code using programming languages, enabling a computer that understands zeros and ones to execute programs and tracing the first three generations.

Machine language was the first programming language, made of zeros and ones, understood directly by hardware, no translation overhead, offering fast execution but lacking human readability and universality across processors.

Assembly language provides a human readable form of machine code using mnemonic codes like add and multiply, and an assembler translates it into machine code with a 1-to-1 correspondence.

Explain how high level languages like C, C++, Java, and Python are portable and hardware independent, reduce development time, and compilers translate to assembly and machine code.

Explore the computer level hierarchy bridging hardware binary language and human languages by layering instruction sets and virtual machines (L1, L2, L3, … Ln) to translate programs into binary.

Apply hierarchical design by translating a program from a top level language down through L3 to L2 to L1 to L0, with hardware at the bottom executing instructions.

Use hierarchical design to divide the computer system into manageable layers, enabling independent implementation, while each layer abstracts the layers below so higher layers interact only with the adjacent layer.

Explore the six-level computer level hierarchy, from digital logic and registers to the ISA, OS services, assembly language, and high-level languages like C++ and Java.

explain the computer level hierarchy from level five high-level language through compiler and assembler to level three machine code, level two iso, level one microarchitecture, and level zero digital logic.

Explore the equivalence of hardware and software, and how each can be implemented in the other. Assess how speed and cost guide whether to implement functionality in hardware or software.

Explore the von Neumann machine model, detailing the CPU with the ALU and register file, main memory, control unit, program counter, and input/output interfaces, plus fetch and decode operations.

Describe how a Von Neumann machine executes instructions through fetch-decode-execute cycle, using the program counter to fetch, decode operands from registers or memory, execute in the ALU, and store results.

Demonstrate the fetch-decode-execute cycle with a RAM-based program, where the control unit fetches instructions via the program counter, loads X and Y into registers, and uses ALU to add them.

Explore multicore processors on a single chip with private and shared caches that enable true parallelism for multi-threaded work, with i3/i5/i7 indicating relative power, and generation by leading digits.

Explore the spectrum of processors—from disposable RFID tags to microcontrollers in devices, portable computers, game-optimized CPUs, graphics cards and servers, to supercomputers and mainframes.

Explore binary numbers and arithmetic, non-negative and signed integers, fractions and floating point, plus image, sound, and character representations, with bits, bytes, and word sizes defined by architecture.

Explore base-10 numbers and decimal representation by examining non-negative integers of infinite length, powers of ten, and how to compute magnitude, with a preview of fixed-length 16-bit and other bases.

Learn binary numbers, base two, using zeros and ones, compute decimal values by summing powers of two, and memorize common powers up to 2^10 (1024) and 2^11 (2048).

Convert binary numbers to decimal by multiplying each digit by its corresponding power of two, illustrated with the example 101101 equaling 45 in base ten.

Explore decimal to binary conversion by applying subtraction and division methods to convert a decimal number into binary.

Apply the subtraction method to convert decimal to binary by subtracting the largest power of two and marking bits, as demonstrated with 90 and the result 1011010.

Learn how to convert decimal to binary using the division by two method, tracking remainders to build the binary digits, as exemplified by 177 becoming 10110001.

Convert a decimal number to binary using the long division method by two, showing step by step divisions and remainders read bottom-up to produce 111101001.

Explore hexadecimal numbers in base 16, with digits 0-9 and a-f. Learn to distinguish hex from decimal using the 0x prefix and group four bits to translate binary to hex.

Convert binary to hexadecimal by forming four-bit groups from the right and padding with zeros on the left; the example yields 351b and introduces octal conversion by grouping threes.

Translate decimal 489 to hexadecimal by converting to binary and grouping four bits at a time, yielding the hex value 1e9.

Explore how fixed length integers, limited by n bits, express nonnegative values from 0 to 2^n minus 1 and how C++ data types allocate memory in bytes.

Explore basic binary addition by comparing zero and one sums, illustrate carries, and show eight-bit overflow with examples like 214 plus 93 equaling 307.

Explain how binary addition works, including carries and the concept of overflow when adding two eight-bit numbers that produce a nine-bit result.

automatic overflow occurs when a result exceeds the available space; in C++, detection is not guaranteed, so check user input bounds to prevent memory corruption and security hazards.

Learn to detect potential overflows in C++ by checking against maximum values (e.g., 0 to 65535) before operations like addition and multiplication, and guard increments to keep code safe.

Explore signed magnitude representation for negative integers, using a sign bit and magnitude bits, illustrated by -43. Understand how two zeros arise and why method is not used in practice.

Learn twos complement representation, where positive numbers match unsigned values and negatives use a leftmost sign bit; eight-bit limits include 127 and -128, and a method to compute it.

Explore the two's complement representation range for signed numbers, using eight bits to show the bounds -2^(n-1) to 2^(n-1)-1 and how the leftmost bit indicates sign.

Express positive numbers in two's complement, identical to unsigned representation. For negatives, flip bits, add one, and see examples like -5 and -43 to illustrate the symmetry.

Determine the magnitude by the sign bit; for positives, sum bits times powers of two; for negatives, convert to the positive using two's complement before summing.

See how two's complement addition uses the sign-bit carry-in and carry-out to detect overflow, by adding 75 and -39 in eight bits.

Explore twos complement addition with an 8-bit example: adding 107 and 46 reveals carry in, no carry out, and overflow beyond the -128 to 127 range.

Determine overflow in two's complement addition by comparing carry into and out of the sign bit; positive and negative addends never overflow, while same-sign adds may.

Explore two's complement addition in an eight-bit space by solving three one-byte additions and identifying overflow using the carry-in and carry-out rule.

Learn zero extension and sign extension for binary numbers, extending unsigned values with zeros and signed values by repeating the sign bit in larger memory spaces, as in two's complement.

Explore subtraction, multiplication, and division of binary numbers, using two's complement for sign handling, long multiplication, and caution against division by zero.