Systems Foundations · core
Data Representation
Binary and hexadecimal, two's complement, IEEE-754 floating point, Unicode, byte order, and serialized bytes.
Mental model
Bits have no meaning until a representation gives them one. Width, signedness, byte order, numeric format, and text encoding are part of every data contract; the same bytes can describe different values when either side assumes a different representation.
How to study Data Representation
Begin by restating the mental model in your own words, then connect it to a concrete system you have built or operated. Name the mechanism, the constraint it addresses, and the trade-off it introduces. Use Computer Systems: A Programmer's Perspective — Student Site to check details, but close the source before writing your explanation. Retrieval is the learning step; rereading is only preparation.
Next, compare Data Representation with Program Memory Model, Compute, Memory & Storage Hierarchy. Ask what changes in correctness, latency, resource use, operability, and failure recovery. Complete Encode a binary compatibility fixture and preserve the command, input, output, and one failed attempt as evidence. Finish by explaining the idea without jargon to someone who has not studied the track.
Proof of understanding
- Explain the mechanism from first principles and identify the state it reads or changes.
- Give one situation where the concept is the right choice and one where it is not.
- Predict a realistic failure mode before running the drill, then compare the prediction with evidence.
- Connect the result to a roadmap or build artifact instead of treating the concept as isolated trivia.
Where it matters
Binary protocols, database pages, file formats, model tensors, network packet inspection, serialization compatibility, and numerical debugging.
Common mistakes
- Treating a hex dump as a value without stating width, signedness, and byte order
- Comparing floating-point results as if every decimal fraction has an exact binary representation
- Confusing Unicode code points with UTF-8 bytes or fixed-width characters
Learn from primary sources
Practice and explain it back
Encode a binary compatibility fixture
Implement encodeRepresentations() without hard-coding the returned fixture. Return lowercase hexadecimal strings for four values: signed16Hex for -42 encoded as a 16-bit two's-complement integer, float32Hex for 0.15625 encoded as IEEE-754 binary32, utf8Hex for the string A€, and littleEndianHex for the 32-bit value 0x12345678 written little-endian.
Expected evidence: An object with signed16Hex, float32Hex, utf8Hex, and littleEndianHex derived from the requested representations.
Open the interactive drill →Review prompts
- A packet contains the bytes d6 ff, and one service reads -42 while another reads 65,494. Explain how both results are possible and what the protocol must specify to make the value unambiguous.
Build evidence
Synthesize: Systems Foundations
Build a tiny HTTP/1.1 static-file server on raw TCP sockets without a framework or high-level HTTP server library. Parse requests, serve bounded files, handle partial I/O, inject failures, measure the result, and explain how the operating system, network, memory, concurrency, and storage paths interact.
- Accepts TCP connections, parses a bounded HTTP GET request, serves fixture files, and returns explicit errors for malformed requests, missing files, and path traversal attempts
- Names and implements a concurrency model with connection, request-size, timeout, and resource limits, including correct handling of partial reads and writes
- Injects at least a slow client, malformed request, or interrupted transfer and demonstrates bounded failure and recovery
- Reports a reproducible workload with throughput, p50/p95 latency, peak memory, and open-connection observations
- Explains the loader, process, syscall, buffer, filesystem, TCP, and scheduling path in a concise architecture note
Trace a Tensor: Diagnose and Optimize One Workload
Trace one tensor-producing model operation from its numerical representation and computation graph through memory movement, kernel execution, engine scheduling, and request-level serving. Build or precisely model a reproducible workload, identify its dominant bottleneck, apply one justified optimization, and defend the resulting quality, latency, resource, and cost trade-offs.
- Maps each lifecycle layer to the data representation, owner, work performed, and observable evidence
- Runs or precisely models one reproducible workload and captures a before profile with latency and memory or bandwidth evidence
- Diagnoses whether the dominant constraint is compute, memory movement, launch overhead, scheduling, or request shape
- Applies one kernel, model-format, memory, or scheduling optimization and reports before/after measurements
- Verifies output quality or numerical correctness and explains one trade-off, failure mode, or remaining risk
Prerequisites
None assigned yet.