Subject: Compulsory Maths

Binary number system consists of two digits 0 and 1 and its base is 2. Each digit or bit in binary number system can be 0 or 1. Digital computer represents all kinds of data and information in the binary system.

110011_{2} = 1× 2^{5} + 1× 2^{4} + 0× 2^{3} + 0× 2^{2} + 1× 2^{1} + 1× 2^{0}In order to convert a binary number into a decimal, it is expanded in the power of 2. Then by simplifyingthe expanded form of the binary number, we obtain a decimal number. For example,

1011_{2} = 1× 2^{3} + 0× 2^{2} + 1× 2^{1} + 1× 2^{0}

= 8 + 0 + 2 + 1

∴ 1011_{2} = 11

= 32 + 16 + 0 + 0 + 2 + 1

∴ 110011_{2} = 51

We can convert decimal number into a binary number by using the place value table of the binary system. For example:

Convert 30 into binary system

2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2 |

32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 | 1 | 1 | 0 |

From the table:

or, 30 = 1× 16 + 1× 8 + 1× 4 + 1× 2 + 1× 1

or, 30 = 1× 2^{4} + 1× 2^{3} + 1× 2^{2} + 1× 2^{1} + 1× 2^{0}

∴ 30 = 11110_{2}

**Alternative method**We must divide the given number successively by 2 in order to convert decimal number into binary number. The remainder obtained in each successive division is listed in a separate column. For example:

- Binary number system consists of two digits 0 and 1 and its base is2.
- Each digit or bit in binary number system can be 0 or 1.
- Digital computer represents all kinds of data and information in the binary system.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

Convert binary numbers into decimal numbers.

1110_{2}

Solution:

1110_{2 }= 1 × 2^{3 }+ 1 × 2^{2} + 1 × 2^{1} + 0 × 2^{0}

= 1 × 8 + 1 × 4 + 1 × 2 + 0

= 8 + 4 + 2

= 14

∴ 1110_{2 }= 14

Convert binary numbers into decimal numbers.

101101_{2}

Solution:

101101_{2 }= 1 × 2^{5} + 0 × 2^{4} + 1 × 2^{3} + 1 × 2^{2} + 0 × 2^{1} + 1 × 2^{2}

= 1 × 32 + 0 + 1 × 8 + 1 × 4 + 0 + 1 × 1

= 32 + 8 + 4 + 1

= 45

∴ 101101_{2 }= 45

Convert decimal numbers into binary numbers.

25

Solution:

2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |

32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 | 0 | 0 | 1 |

25 = 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1

= 1 × 2^{4} + 1 × 2^{3} + 0 × 2^{2} + 0 × 2^{1} + 1 × 2^{0}

= 11001

∴ 25 = 11001_{2}

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