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Operating System | Week 29 Topics1 Quiz
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Computer Memory: Primary And Secondary Memory | Week 35 Topics1 Quiz
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Computer Memory II: Secondary Memory (Backing Storage) | Week 42 Topics1 Quiz
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Number System I | Week 54 Topics1 Quiz
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Number System II | Week 63 Topics1 Quiz
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Units of Storage In Computer | Week 72 Topics1 Quiz
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Problem Solving Skills With Computer | Week 85 Topics1 Quiz
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Computer Programming Languages | Week 93 Topics1 Quiz
Quizzes
Topic Content:
- Meaning of Number System
- Types of Number Systems
- binary, decimal, octal, hexadecimal
- Binary-coded Decimal (BCD)
- Summary
A computer can understand only a few symbols called digits and these symbols describe different values depending on the position they hold in the number. In general, the binary number system is used in computers. However, the octal, decimal and hexadecimal systems are also used sometimes.
Numbers, alphabets, and symbols that are sent to the CPU must, first of all, be changed to binary digits before any actions can be taken by the CPU. The section of the CPU that does the conversion is called the decoder.
The number system, therefore, is the way in which digital computers handle numerical values.
Types of Number Systems:
There are various types of number systems in mathematics. The most common number system types used are:
- Binary number system (Base – 2)
- Octal number system (Base – 8)
- Decimal number system (Base – 10)
- Hexadecimal number system (Base – 16)
Binary System:
The binary numeral system is the base 2 number system. It is very important because it is used by computers for numerical calculations. Binary numbers are made up of two digits: 1 and 0. A computer contains a number of switches. Each switch is either ‘on’ or ‘off’. ‘On’ represents ‘1’, and ‘Off’ represents ‘0’.
All computer systems irrespective of their shapes and sizes are based on the binary system.
Octal System:
The octal numeral system is the base-8 number system. It means that it has 8 digits 0, 1, 2, 3, 4, 5, 6, and 7. This is written using eight distinct symbols (0-7)
When counting and the number is up to 7, it implies that we have run out of digits.
Decimal / Denary System:
The system of counting in tens is called the decimal system. It has a base of 10. In the decimal system, there are 10 digits which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Here, you count up from 0 to 9 and then reset your number to 0, and carry 1 into another column.
Hexadecimal System:
This is a number system with 16 as the base. The 16 digits and characters used in the hexadecimal system (HEX) are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Symbols A, B, C, D, E, and F are equivalent to decimal 10, 11, 12, 13, 14, and 15 respectively.
| Hexadecimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Binary-coded Decimal (BCD):
The following are some decimal numbers with their equivalent binary codes.
Binary-coded Decimal:
| Decimal: | Binary Code: |
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
Summary:
Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system.
There are various types of number systems in mathematics. The four most common number system types are:
- Decimal number system (Base – 10)
- Binary number system (Base – 2)
- Octal number system (Base -8)
- Hexadecimal number system (Base – 16)
| Number system: | Base: | Used digits: | Example: |
| Binary | 2 | 0,1 | (11110000)2 |
| Octal | 8 | 0,1, 2, 3, 4, 5, 6, 7 | (360)8 |
| Decimal | 10 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 | (240)10 |
| Hexadecimal | 16 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F | (F0)16 |