7. 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 in 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 3B8. (a) How many 2-digit hexadecimals are there in which the first digit is E or F? Explain your answer in terms of the additive principle (using either events or sets). (b) Explain why your answer to the previous part is correct in terms of the multiplicative principle (using either events or sets). Why do both the additive and multiplicative principles give you the same answer? (c) How many 3-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? Explain.
7. 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 in 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 3B8. (a) How many 2-digit hexadecimals are there in which the first digit is E or F? Explain your answer in terms of the additive principle (using either events or sets). (b) Explain why your answer to the previous part is correct in terms of the multiplicative principle (using either events or sets). Why do both the additive and multiplicative principles give you the same answer? (c) How many 3-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? Explain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:7. 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 in 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 3B8.
(a) How many 2-digit hexadecimals are there in which the first digit is E or F? Explain your answer
in terms of the additive principle (using either events or sets).
(b) Explain why your answer to the previous part is correct in terms of the multiplicative principle
(using either events or sets). Why do both the additive and multiplicative principles give you the
same answer?
(c) How many 3-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? Explain.
(d) How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?
Explain.
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