Fundamentals of Computers and Number Systems
Fundamentals of Computers and Number Systems
This domain checks your grasp of computer organisation and data representation. Questions often cover the input-process-output model, generations and classifications of computers, memory units, logic gates, and conversions between binary, octal, decimal and hexadecimal. You must be able to show working, not just state an answer.
Core rules
- Every positional system uses a base: binary 2, octal 8, decimal 10, hexadecimal 16.
- For a decimal integer, divide repeatedly by the target base and read remainders from bottom to top.
- For a decimal fraction, multiply repeatedly by the base and read integer parts from top to bottom.
- Group binary bits in threes for octal and fours for hexadecimal, starting at the radix point and padding with zeros.
- In 8-bit two's complement the range is -128 to +127. To negate, invert all bits and add 1.
- 1 byte = 8 bits, 1 nibble = 4 bits, and exam questions conventionally use 1 KB = 1024 bytes.
Worked example
Convert 45 in decimal to binary and hexadecimal. Divide by 2: 45 gives 22 remainder 1, 22 gives 11 remainder 0, 11 gives 5 remainder 1, 5 gives 2 remainder 1, 2 gives 1 remainder 0, and 1 gives 0 remainder 1. Reading upward gives 101101 in binary. Check: 32+8+4+1=45. Group as 0010 1101; the groups are 2 and 13, so the hexadecimal answer is 2D. The grouping works because four binary bits make one hexadecimal digit.
Traps
Reading remainders top-to-bottom reverses the number. Writing 13 as a single hex character is invalid; use D. Do not mix sign-magnitude with two's complement. For fractions, stop only at the requested precision, and remember that 0.1 in decimal does not terminate in binary.