# Spring 2001 CSCI 255 Homework 1 Solution

## Problem 1

Convert the following numbers from decimal into ten-bit
twos-complement notation.

431 | 0110101111 |

-400 | 1001110000 |

1 | 0000000001 |

-11 | 1111110101 |

## Problem 2

Convert the following ten-bit twos-complement numbers
into decimal numbers.

0011001100 | 204 |

1110001110 | -114 |

0000000000 | 0 |

1111111100 | -4 |

## Problem 3

What are the largest and smallest numbers that can be
expressed as a six-bit twos-complement number?

The smallest is -32 (10000) and the largest is 31 (011111).
In general, if `n` is the width of the twos complement
number, the smallest possible number is -2^{n-1}
and the largest possible number is 2^{n-1}-1,

## Problem 4

Express the following decimal numbers in base 6: