Computer Fundamentals and Number Systems
Computer Fundamentals and Number Systems
This domain tests how a computer represents and manipulates data: generations and classifications, hardware/software boundaries, units, and number-system conversions. Expect direct conversion and binary-arithmetic questions rather than definitions alone.
Core rules
- Decimal is base 10; binary base 2; octal base 8; hexadecimal base 16. Hex digits are 0–9 and A–F.
- To convert decimal to another base, divide repeatedly by the target base and read remainders upward.
- To convert binary to hex, group bits in fours from the radix point; to octal, group in threes. Pad with leading or trailing zeros as needed.
- A byte is 8 bits; 1 KB = 1024 bytes in the binary-memory convention, while storage marketing may use 1000.
- In signed binary, the leftmost bit is the sign bit in sign-magnitude; two’s complement represents negatives.
Worked example
Convert decimal 45 to binary and hex. Divide by 2: 45→22 remainder 1, 22→11 remainder 0, 11→5 remainder 1, 5→2 remainder 1, 2→1 remainder 0, 1→0 remainder 1. Read remainders upward: 101101₂. Group from the right: 0010 1101, giving 2D₁₆. Check: 32 + 8 + 4 + 1 = 45. Grouping is why hex is compact.
Traps
Reading remainders downward gives the bit-reversal error. For fractions, multiply the fractional part by the base and read integer parts forward. Do not mix 1000 and 1024 without stating the convention. In two’s complement, the sign bit has negative weight, not just a flag.