Fundamentals of Computers and Number Systems
What this domain tests
The exam checks whether you can describe how a digital computer is organised and convert between the number systems used to represent data. Expect questions on the stored-program concept, CPU–memory–I/O structure, memory units, generations of computers, positional number systems, binary arithmetic, complements, and character codes such as ASCII and Unicode.
Core rules
- A positional system with radix r uses digits 0 to r−1. Binary r=2, octal r=8, decimal r=10, hexadecimal r=16 - hex needs A–F for 10–15.
- To convert decimal to base r, divide repeatedly by r and read remainders bottom-up.
- Binary to octal/hex: group bits in 3s or 4s from the right, padding with leading zeros.
- In 8-bit two's complement, positives are 0–127; negatives are formed by inverting bits and adding 1. The range is −128 to +127.
- 1's complement has two zeros (+0 and −0); 2's complement has one, which is why hardware uses it.
Worked example
Convert decimal 156 to binary and hexadecimal. 156 ÷ 2 = 78 remainder 0; 78÷2=39 r0; 39÷2=19 r1; 19÷2=9 r1; 9÷2=4 r1; 4÷2=2 r0; 2÷2=1 r0; 1÷2=0 r1. Reading remainders bottom-up gives 10011100₂. Group into 4 bits: 1001 1100 = 9C₁₆. Check: 128+16+8+4 = 156.
Traps that cost marks
Using digit 8 or 9 in octal; reading conversion remainders top-down; padding bit groups on the wrong side; confusing BCD (each decimal digit in 4 bits) with pure binary; forgetting that the 2's complement of 0 is 0; writing a hex digit in the wrong case where the format is specified.