Problem 1. 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) where A, B, C, D, E and F represent digits with values 10, 11, 12, 13, 14 and 15, respectively. So for example, a 3 digit hexadecimal number might be 2B8= 8+ (B) 16+ (2) 16² = 8+ (11) 16+ (2) 16² = 696. (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.
Problem 1. 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) where A, B, C, D, E and F represent digits with values 10, 11, 12, 13, 14 and 15, respectively. So for example, a 3 digit hexadecimal number might be 2B8= 8+ (B) 16+ (2) 16² = 8+ (11) 16+ (2) 16² = 696. (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.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:Problem 1.
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}; where A, B, C, D, E and F represent digits with values 10, 11, 12, 13, 14 and 15, respectively. So for example, a 3 digit hexadecimal number might be 2B8 = 8 + (B) 16 + (2) 16^2 = 8 + (11) 16 + (2) 16^2 = 696.
(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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Hexadecimal:
A base-16 numbering scheme is hexadecimal. It allows for the representation of huge integers with fewer digits. Six alphabetic characters, A, B, C, D, E, and F, are followed by 16 symbols, or possible digit values from 0 to 9, in this system.
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