__Binary Conversion __

Power, p | 2 |

0 | 1 |

1 | 2 |

2 | 4 |

3 | 8 |

4 | 16 |

5 | 32 |

6 | 64 |

7 | 128 |

8 | 256 |

9 | 512 |

Fig 2 Some powers of 2

__CONVERSION OF DECIMAL INTEGERS TO BINARY Method __

1- Write out powers of 2 in a line starting at the right with 1. That is write ... 64 32 16 8 4 2 1 (as many as necessary).

2- Subtract these powers of 2 from the number. Each time subtract the largest one which will go.

3- When a power is subtracted write a 1 under that power, otherwise write a 0.

__Worked question __

Convert the decimal number 71 to binary.

64 32 16 8 4 2 1 (The line of powers)

1 0 0 0 1 1 1 (The Is and Os written down while subtracting)

71-

__64 __

7-

__4 __

3-

__2 __

Answer: 71_{10}= 1000111_{2}

CONVERSION OF BINARY INTEGERS TO DECIMAL

__Method __

1- Write powers of 2 above the digits of the binary numbers. Start at the right-hand end. That is write ... 64 32 16 8 4 2 1 (as many as necessary).

2- Write down the powers of 2 which are above a 1 in the binary number. Add them up to obtain the answer.

__Worked question __

Convert the binary number 1101101 to decimal.

64 32 16 8 4 2 1

1 1 0 1 1 0 1

Number = 64+32+8+4+ 1

=109

Answer: 1101101_{2 }= 109_{10}