Introduction to Computers and Number Systems
Introduction to Computers and Number Systems
This domain tests how a computer accepts, stores and processes data, and how the same quantity is represented in different bases. Expect questions on hardware and software, input–process–output, storage units, and conversions among binary, octal, decimal and hexadecimal.
Core rules
- A computer system is hardware plus software; the CPU executes instructions, main memory holds active programs, and secondary storage is non-volatile.
- A base-r system uses r digits, from 0 to r−1. Binary is base 2, octal base 8, decimal base 10, and hexadecimal base 16, where A=10 through F=15.
- Decimal to base-r: divide repeatedly by r and read remainders upward. Base-r to decimal: expand each digit as digit × r^position.
- Binary to octal or hexadecimal: group bits in 3s or 4s from the binary point, padding with zeros at the ends.
- 1's complement flips bits; 2's complement flips bits and adds 1, and is used for signed integer subtraction.
Worked example
Convert decimal 45 to binary and hexadecimal. 45 ÷ 2 = 22 rem 1; 22 ÷ 2 = 11 rem 0; 11 ÷ 2 = 5 rem 1; 5 ÷ 2 = 2 rem 1; 2 ÷ 2 = 1 rem 0; 1 ÷ 2 = 0 rem 1. Read remainders upward: 101101₂. Group from the right into nibbles: 0010 1101. 0010 = 2 and 1101 = D, so the answer is 2D₁₆. Check: 2×16 + 13 = 45.
Traps
- Reading remainders downward gives the bit-reversed answer.
- Do not write subscript 10 on a binary value; the base label is part of the answer.
- In hexadecimal, 10 is A, not the decimal ten; decimal 16 is 10₁₆.
- Pad the left of a binary group, not the right, before converting to hexadecimal.
- Do not confuse storage units: 1 byte is 8 bits, and 1 KB is 1024 bytes in the binary convention used in this syllabus.