Summary
Number systems are essential for data representation in computers, using binary, denary, and hexadecimal systems to process and store data.
- Binary System — a base 2 number system using only 0s and 1s. Example: 10101111 is a binary number.
- Denary System — a base 10 number system using digits 0-9. Example: 251 is a denary number.
- Hexadecimal System — a base 16 number system using digits 0-9 and letters A-F. Example: 21F3A is a hexadecimal number.
- Two's Complement — a method for representing positive and negative binary numbers. Example: 11001111 represents -49 in two's complement.
Exam Tips
Key Definitions to Remember
- Binary System: Base 2 number system using 0s and 1s.
- Denary System: Base 10 number system using digits 0-9.
- Hexadecimal System: Base 16 number system using digits 0-9 and letters A-F.
- Two's Complement: Method for representing positive and negative binary numbers.
Common Confusions
- Confusing binary and hexadecimal conversions.
- Misunderstanding the purpose of two's complement.
Typical Exam Questions
- How do you convert the binary number 10101111 to denary? Answer: 175
- What is the hexadecimal representation of the binary number 110011110011? Answer: CF3
- How do you add two 8-bit binary numbers, such as 00100111 and 01001010? Answer: 01110001
What Examiners Usually Test
- Ability to convert between binary, denary, and hexadecimal systems.
- Understanding of binary addition and overflow.
- Knowledge of logical binary shifts and their effects.