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We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different "digits" {0, 1,...,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0, 1,...,9, A, B, C, D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8. a. How many 4-digit hexadecimals are there in which the first digit is E or F? 8192 b. How many 5-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? c. How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?

We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different "digits" {0, 1,...,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0, 1,...,9, A, B, C, D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8. a. How many 4-digit hexadecimals are there in which the first digit is E or F? 8192 b. How many 5-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? c. How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**Understanding Hexadecimal Numbers** Hexadecimal numbers, or base 16 numbers, provide a method of counting and representing values using 16 distinct digits. These digits include the numbers {0, 1, …, 9} and the letters {A, B, C, D, E, F}, where each letter represents numbers 10 through 15 in decimal form. This system can be quite useful, especially in fields like computer science. ### Examples and Exercises 1. **Four-Digit Hexadecimals with First Digit E or F:** - Consider four-digit hexadecimal numbers starting with either E or F. - Given that there are 16 digits available for each position, there are 8192 possible combinations. 2. **Five-Digit Hexadecimals Starting with a Letter and Ending with a Numeral:** - Five-digit numbers that start with a letter (A-F) and end with a numeral (0-9) consist of exploring various combinations. - Enter a solution based on understanding the positional choices up front. 3. **Three-Digit Hexadecimals Starting or Ending with Specific Characters:** - Three-digit numbers can begin with a letter (A-F) or end with a numeral (0-9), or satisfy both conditions. - This problem involves considering various subsets of possibilities and calculating accordingly. This exploration into hexadecimal systems showcases differing numeric bases outside of the usual decimal system, enhancing computational and mathematical perspectives.
Transcribed Image Text:**Understanding Hexadecimal Numbers** Hexadecimal numbers, or base 16 numbers, provide a method of counting and representing values using 16 distinct digits. These digits include the numbers {0, 1, …, 9} and the letters {A, B, C, D, E, F}, where each letter represents numbers 10 through 15 in decimal form. This system can be quite useful, especially in fields like computer science. ### Examples and Exercises 1. **Four-Digit Hexadecimals with First Digit E or F:** - Consider four-digit hexadecimal numbers starting with either E or F. - Given that there are 16 digits available for each position, there are 8192 possible combinations. 2. **Five-Digit Hexadecimals Starting with a Letter and Ending with a Numeral:** - Five-digit numbers that start with a letter (A-F) and end with a numeral (0-9) consist of exploring various combinations. - Enter a solution based on understanding the positional choices up front. 3. **Three-Digit Hexadecimals Starting or Ending with Specific Characters:** - Three-digit numbers can begin with a letter (A-F) or end with a numeral (0-9), or satisfy both conditions. - This problem involves considering various subsets of possibilities and calculating accordingly. This exploration into hexadecimal systems showcases differing numeric bases outside of the usual decimal system, enhancing computational and mathematical perspectives.
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