30a-Primes

# 30a-Primes - Primes Introduction Discrete Mathematics...

This preview shows pages 1–7. Sign up to view the full content.

Primes Discrete Mathematics

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discrete Mathematics – Primes 30-2 Previous Lecture Integers Divisor, remainders Properties of divisibility The division algorithm
Discrete Mathematics – Primes 30-3 Representation of Integers In most case we use decimal representation of integers. For example, 657 means 6 100 + 5 10 + 7 = Let b be a positive integer greater than 1. Then if n is a positive integer, it can be expressed uniquely in the form where k is a nonnegative number, are nonnegative integers less than b, and Such a representation of n is called the base b expansion of n, denoted by

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discrete Mathematics – Primes 30-4 2 0 2 1 1 2 10 20 0 41 1 2 2 165 2 82 Binary Expansion Important case of a base is 2. The base 2 expansion is called the binary expansion of a number Find the binary expansion of 165 1 165 = 2 82 + 1 2 0 82 = 2 41 + 0 41 = 2 20 + 1 20 = 2 10 + 0 2 0 5 10 = 2 5 + 0 5 = 2 2 + 1 2 = 2 1 + 0 1 = 2 0 + 1
Discrete Mathematics – Primes 30-5 Hexadecimal Expansion Using A, B, C, D, E, F for 10, 11, 12, 13, 14, 15, respectively, find the base 16 expansion of 175627

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discrete Mathematics – Primes 30-6 Primes Every integer n (except for 1 and -1) has at least 2 positive divisors, 1 and n (or -n).
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 15

30a-Primes - Primes Introduction Discrete Mathematics...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online