3. Integers - MATH 224 Discrete Mathematics Integers and...

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1 08/27/09 MATH 224 – Discrete Mathematics Integers and Computers Integers and number theory are important building blocks for computer science. (Number theory deals with the properties of integers.) Why are integers so important in computer science? Consider the memory of a computer. What does it store? Just sequences of zeros and ones. When put all together the total memory may be interpreted as one large binary integer. How are integers most commonly represented in memory? What is the 32 bit representation of 500? What is the 32 bit representation of -500?
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2 08/27/09 MATH 224 – Discrete Mathematics Integers and Computers How are letters (characters) stored inside a computer’s memory? How are floating point numbers (i.e. numbers with fractional parts) stored? How are text files; Word documents; C++ programs; and machine instructions stored in memory? At the lowest level, digital computers can only work with numbers. How is audio stored with integers? How are photographs stored with integers? Can color be represented by an integer? How are videos stored as integers?
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3 08/27/09 MATH 224 – Discrete Mathematics Integer Terminology Integers may be classified as either prime numbers or composite numbers. What is a prime number, and what is a composite number? The following is often referred to as the Fundamental Theorem of Arithmetic . Every positive integer larger than 1 may be expressed as a single prime number or a unique product of primes. This product is called the prime factorization of an integer. Those numbers that are not primes, having two or more primes in their prime factorization, are called composite numbers. What about negative integers less than 1. Do they have a unique prime factorization? Is there a way to make the factorization unique?
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4 08/27/09 MATH 224 – Discrete Mathematics Division Algorithm (uniqueness of modulus) The so called division algorithm is not really an algorithm, but instead states a property of integers. It states that when an integer
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3. Integers - MATH 224 Discrete Mathematics Integers and...

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