FTCE Computer Science cheat sheet

Binary place values double leftward: 1, 2, 4, 8, 16, 32, 64, 128; 1101₂ = 8 + 4 + 1 = 13₁₀.

Hex digit = exactly 4 bits, so one byte always renders as two hex digits (255₁₀ = 11111111₂ = FF₁₆).

Two's complement: invert all bits and add 1 to negate; an n-bit signed range is −2^(n−1) to 2^(n−1) − 1.

Boolean identities: De Morgan gives ¬(A ∧ B) = ¬A ∨ ¬B and ¬(A ∨ B) = ¬A ∧ ¬B; XOR is 1 only when inputs differ.

Data structures by cost: array index O(1); balanced BST search O(log n); hash table average O(1), worst O(n) under collisions.

Stack is LIFO (push/pop), queue is FIFO (enqueue/dequeue); recursion uses the call stack, breadth-first search uses a queue.

Sorting: bubble/insertion/selection are O(n²); merge and heap sort are O(n log n); quicksort averages O(n log n), worst O(n²).

Abstraction, encapsulation, inheritance, and polymorphism are the four OOP pillars; overloading is compile-time, overriding is runtime dispatch.

Compiler translates the whole source to machine code before execution; interpreter executes statement by statement, so errors surface at runtime.

Decomposition breaks a problem into subproblems; pattern recognition finds reusable regularities; abstraction removes detail; algorithm design orders steps.

Algorithm properties: finite (terminates), definite (unambiguous steps), has input/output, and is effective (each step is executable).

Linear search is O(n) on any list; binary search is O(log n) but requires a sorted array and random access.

Trace a loop by tabulating variable values per iteration; off-by-one errors show as one extra or one missing iteration.

Flowchart symbols: oval = start/end, parallelogram = input/output, rectangle = process, diamond = decision, arrow = control flow.

Pseudocode is language-neutral; convert it by mapping sequence to statements, selection to if/else or switch, iteration to for/while.

Recursive solution needs a base case and a recursive case that moves toward the base; missing base case causes stack overflow.

Big-O describes growth of the dominant term as input grows; constants and lower-order terms are dropped (3n² + 5n → O(n²)).

Test cases should cover normal input, boundary values, and invalid input; a boundary error often appears at the first or last element.

Variable scope: local variables exist only inside their block; parameters are local; global/static variables persist for the program lifetime.

Pass by value copies the argument; pass by reference passes the address, so callee changes are visible to the caller.

Loop selection rule: use for when the iteration count is known, while when it depends on a condition, do-while when the body must run at least once.

Array indices are zero-based in Java, C, C++, and Python; accessing index equal to length throws an out-of-bounds error.

String comparison uses equals() in Java, not ==, which compares object references rather than character content.

Exception handling: try holds risky code, catch handles a thrown exception, finally always runs; unchecked exceptions need not be declared.

SDLC phases: requirements, design, implementation, testing, deployment, maintenance; maintenance typically consumes the largest share of lifetime cost.

Version control commits record snapshots; branches isolate work; merging combines histories and conflicts arise when the same lines changed.

Agile delivers working increments in short iterations with continuous feedback; waterfall sequences phases with heavy upfront specification.

CPU cycle: fetch instruction from memory, decode it, execute it, store the result; the program counter holds the next address.

Memory hierarchy by speed and cost: registers, cache (L1/L2/L3), RAM, SSD/HDD; each lower level is larger and slower.

RAM is volatile and holds running programs; ROM is nonvolatile; secondary storage keeps data when power is off.

Operating system duties: process scheduling, memory management, file systems, device drivers, and user/security management.

Number storage: a signed 8-bit value spans −128 to 127; overflow wraps or errors when a result exceeds the representable range.

ASCII uses 7 bits for 128 characters; Unicode assigns code points for all scripts, and UTF-8 encodes them in 1–4 bytes.

Logic gates: AND outputs 1 only if both inputs are 1, OR if either is 1, NOT inverts, XOR if inputs differ; combine gates to build adders.

Machine cycle timing relates to clock speed; more cores allow parallel processes but do not automatically speed a single-threaded program.

OSI layers bottom-up: Physical, Data Link, Network, Transport, Session, Presentation, Application; TCP/IP collapses these to four.

IP addresses identify hosts; DNS resolves domain names to IP addresses; DHCP assigns addresses automatically.

TCP is connection-oriented and reliable with acknowledgments and retransmission; UDP is connectionless with lower overhead.

Private IPv4 ranges: 10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16; a /24 subnet masks 255.255.255.0 and yields 254 usable hosts.

HTTP/HTTPS run over TCP; HTTPS adds TLS encryption; port 80 is HTTP, 443 HTTPS, 25 SMTP, 53 DNS, 22 SSH.

Topologies: star fails gracefully per node but depends on the central switch; mesh offers redundant paths at higher cabling cost.

Security controls: encryption protects confidentiality, hashing verifies integrity, firewalls filter traffic, MFA strengthens authentication.

Computing impacts: automation shifts employment, digital divides limit access, and data collection raises privacy and consent questions.

Acceptable-use and IP law: copyright protects expression, patents protect inventions, and fair use is a limited, factor-based exception.

Binary place values double leftward: 1, 2, 4, 8, 16, 32, 64, 128; 1101₂ = 8 + 4 + 1 = 13₁₀.

Hex digit = exactly 4 bits, so one byte always renders as two hex digits (255₁₀ = 11111111₂ = FF₁₆).

Two's complement: invert all bits and add 1 to negate; an n-bit signed range is −2^(n−1) to 2^(n−1) − 1.

Boolean identities: De Morgan gives ¬(A ∧ B) = ¬A ∨ ¬B and ¬(A ∨ B) = ¬A ∧ ¬B; XOR is 1 only when inputs differ.

Data structures by cost: array index O(1); balanced BST search O(log n); hash table average O(1), worst O(n) under collisions.

Stack is LIFO (push/pop), queue is FIFO (enqueue/dequeue); recursion uses the call stack, breadth-first search uses a queue.

Sorting: bubble/insertion/selection are O(n²); merge and heap sort are O(n log n); quicksort averages O(n log n), worst O(n²).

Abstraction, encapsulation, inheritance, and polymorphism are the four OOP pillars; overloading is compile-time, overriding is runtime dispatch.

Compiler translates the whole source to machine code before execution; interpreter executes statement by statement, so errors surface at runtime.

Decomposition breaks a problem into subproblems; pattern recognition finds reusable regularities; abstraction removes detail; algorithm design orders steps.

Algorithm properties: finite (terminates), definite (unambiguous steps), has input/output, and is effective (each step is executable).

Linear search is O(n) on any list; binary search is O(log n) but requires a sorted array and random access.

Trace a loop by tabulating variable values per iteration; off-by-one errors show as one extra or one missing iteration.

Flowchart symbols: oval = start/end, parallelogram = input/output, rectangle = process, diamond = decision, arrow = control flow.

Pseudocode is language-neutral; convert it by mapping sequence to statements, selection to if/else or switch, iteration to for/while.

Recursive solution needs a base case and a recursive case that moves toward the base; missing base case causes stack overflow.

Big-O describes growth of the dominant term as input grows; constants and lower-order terms are dropped (3n² + 5n → O(n²)).

Test cases should cover normal input, boundary values, and invalid input; a boundary error often appears at the first or last element.

Variable scope: local variables exist only inside their block; parameters are local; global/static variables persist for the program lifetime.

Pass by value copies the argument; pass by reference passes the address, so callee changes are visible to the caller.

Loop selection rule: use for when the iteration count is known, while when it depends on a condition, do-while when the body must run at least once.

Array indices are zero-based in Java, C, C++, and Python; accessing index equal to length throws an out-of-bounds error.

String comparison uses equals() in Java, not ==, which compares object references rather than character content.

Exception handling: try holds risky code, catch handles a thrown exception, finally always runs; unchecked exceptions need not be declared.

SDLC phases: requirements, design, implementation, testing, deployment, maintenance; maintenance typically consumes the largest share of lifetime cost.

Version control commits record snapshots; branches isolate work; merging combines histories and conflicts arise when the same lines changed.

Agile delivers working increments in short iterations with continuous feedback; waterfall sequences phases with heavy upfront specification.

CPU cycle: fetch instruction from memory, decode it, execute it, store the result; the program counter holds the next address.

Memory hierarchy by speed and cost: registers, cache (L1/L2/L3), RAM, SSD/HDD; each lower level is larger and slower.

RAM is volatile and holds running programs; ROM is nonvolatile; secondary storage keeps data when power is off.

Operating system duties: process scheduling, memory management, file systems, device drivers, and user/security management.

Number storage: a signed 8-bit value spans −128 to 127; overflow wraps or errors when a result exceeds the representable range.

ASCII uses 7 bits for 128 characters; Unicode assigns code points for all scripts, and UTF-8 encodes them in 1–4 bytes.

Logic gates: AND outputs 1 only if both inputs are 1, OR if either is 1, NOT inverts, XOR if inputs differ; combine gates to build adders.

Machine cycle timing relates to clock speed; more cores allow parallel processes but do not automatically speed a single-threaded program.

OSI layers bottom-up: Physical, Data Link, Network, Transport, Session, Presentation, Application; TCP/IP collapses these to four.

IP addresses identify hosts; DNS resolves domain names to IP addresses; DHCP assigns addresses automatically.

TCP is connection-oriented and reliable with acknowledgments and retransmission; UDP is connectionless with lower overhead.

Private IPv4 ranges: 10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16; a /24 subnet masks 255.255.255.0 and yields 254 usable hosts.

HTTP/HTTPS run over TCP; HTTPS adds TLS encryption; port 80 is HTTP, 443 HTTPS, 25 SMTP, 53 DNS, 22 SSH.

Topologies: star fails gracefully per node but depends on the central switch; mesh offers redundant paths at higher cabling cost.

Security controls: encryption protects confidentiality, hashing verifies integrity, firewalls filter traffic, MFA strengthens authentication.

Computing impacts: automation shifts employment, digital divides limit access, and data collection raises privacy and consent questions.

Acceptable-use and IP law: copyright protects expression, patents protect inventions, and fair use is a limited, factor-based exception.