Computer Architecture and Data Representation
Units and bases
8 bits = 1 byte; 4 bits = 1 nibble = one hex digit. Convert binary to hex by grouping nibbles: 1011 0110 = 0xB6. Know powers of two: 2^10 = 1024 ≈ 1 KB (distinct from decimal 1000 used by storage vendors).
Signed numbers
An n-bit two's complement value ranges from −2^(n−1) to 2^(n−1) − 1. To negate, invert every bit and add 1. When the MSB is set, the value is −2^(n−1) plus the remaining bits: 1101 = −8 + 4 + 0 + 1 = −3; 1111 1111 = −1; 1000 0000 = −128.
CPU and memory
The fetch–decode–execute cycle: the program counter holds the next instruction address, the ALU performs arithmetic and logic, and registers are the fastest storage. Memory hierarchy from fastest to slowest: registers → L1/L2/L3 cache → RAM → SSD/HDD, with cost per byte falling and latency rising as you descend. RISC uses many simple fixed-length instructions; CISC uses fewer, more complex ones. Pipelining overlaps instruction stages; a branch misprediction flushes the pipeline.
Text and bitwise
ASCII: 'A'=65, 'a'=97, '0'=48. Unicode/UTF-8 extends this with variable-width encoding. Bitwise AND/OR/XOR/NOT manipulate masks; left shift by k multiplies by 2^k, right shift divides. Little-endian stores the least significant byte first.
Traps
Confusing 1000 with 1024; forgetting the sign bit when computing ranges; assuming higher clock speed always means a faster machine; treating a 32-bit address space as 32 bytes.
Worked example
Convert 1011 0110 to hex: nibbles 1011 = B and 0110 = 6 → 0xB6. Rule of thumb: group right-to-left in fours, pad the left with zeros.