# Solution for Spring 2002 CSCI 255 Practice Homework 1

## Problem 1

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

 431 0110101111 -500 1000001100 1 0000000001 -17 1111101111

## Problem 2

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

 1011001110 -306 0110101110 430 1000000010 -510 0111111110 510

## Problem 3

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

The smallest is -512 (binary 1000000000) and the largest is 511 (binary 0111111111). In general, if n is the width of the twos complement number, the smallest possible number is -2n-1 and the largest possible number is 2n-1-1,

## Problem 4

Express the following decimal numbers in base 6:

 255 1103 36 100

## Problem 5

Add the following six-bit twos-complement number. Which, if any, of the additions result in an overflow?

 101000 + 111011 100011 011111 + 000111 100110

In the first problem, two negative numbers are added and a negative number is the result. This is not an overflow. In the second problem, two postive numbers are added and a negative number is the result. This is an overflow.