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. The memory inside the computer is constructed in terms of bits, bytes, Nibbles, and words.

**Bit:** A bit stands for Binary digit. It is the smallest unit of data inside one computer.

**Byte: **This is a collection of eight bits.

**Nibble:** This represents a group of 4 bits.

### Word:

A word constitutes the amount of data that a computer can handle in a given operation. The number of bits that constitute a word is called Word length. Different computers have different word lengths, varying from 8 bits to 64 bits. Word lengths are 16, 24, 32, 64 bits.

The larger the word length, the faster the processing speed, and the greater the main storage capacity of the computer, and perhaps the greater the price.

### Octal System:

The binary is a number with base 2. 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 â€˜onâ€™ or â€˜offâ€™. â€˜Onâ€™ represents â€˜1â€™, and â€˜Offâ€™ represents â€˜0â€™.

All computer systems irrespective of their shapes and sizes are based on the binary system.

### Octal System:

This is a number with base 8. 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.

### Binary Code Decimal (BCD)

The following are some decimal numbers with their equivalent binary codes.

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 |

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