Computer Science Fundamentals: Representation, Logic and Architecture
This domain tests the layer below programming: how numbers and characters are stored, how Boolean logic builds circuits, how the von Neumann machine executes instructions, and how operating systems and networks organise resources. Questions are usually short computational items with a single defensible answer.
Core rules
- Binary, octal and hexadecimal: one hex digit equals exactly four bits, so conversion is done by grouping, never by arithmetic on the decimal value.
- Two's complement in n bits covers −2^(n−1) to 2^(n−1) − 1. Negation = invert every bit, then add 1.
- Overflow occurs when the result of adding two operands of the same sign has the opposite sign.
- IEEE 754 floats store sign, biased exponent and mantissa: more exponent bits widen the range, more mantissa bits improve precision. Values such as 0.1 have no exact binary representation.
- Boolean algebra: De Morgan's laws, canonical sum-of-products and Karnaugh simplification.
- von Neumann architecture shares one memory for data and instructions and executes fetch–decode–execute; the cache hierarchy exploits temporal and spatial locality.
- OS: process versus thread, virtual memory and paging, scheduling policies.
- Networks: TCP is connection-oriented and reliable, UDP is not; DNS resolves names; layers map between the OSI and TCP/IP models.
Worked example
Represent −37 in 8 bits. 37 = 0010 0101. Invert: 1101 1010. Add 1: 1101 1011, which is DB in hexadecimal. Check: read as unsigned, 1101 1011 = 219, and 219 + 37 = 256, confirming the two's-complement relationship. The valid 8-bit range is −128 to 127. Adding 100 + 100: 0110 0100 + 0110 0100 = 1100 1000, interpreted as −56, so the sign flipped and overflow is flagged.
Traps that cost marks
Forgetting the +1 after inverting; using sign-magnitude instead of two's complement, which gives a different answer for negative numbers; mixing up 1 KB = 1024 bytes with 1000; assuming ASCII covers all characters (Unicode is needed for Greek and other scripts); and believing that a larger mantissa increases the representable range.