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Question 1 Let a be a hexadecimal string with n-digits. In other words = (1,...,n) where each coor- dinate x is equal to one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Define the weight of a hexadecimal string to be the number of non-zero coordinates. So (A, F, 1, 2, 0) has weight 4 and (1,2,0,0, F) has weight 3. Let hn,k be the number of n-digit hexadecimal strings with weight k. Choose one of the following questions to answer: You do not need to do both. 1. Find a recurrence relation for hn,k. Justify your answer. 2. Find a formula for hn,k. Justify your answer.

Question 1 Let a be a hexadecimal string with n-digits. In other words = (1,...,n) where each coor- dinate x is equal to one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Define the weight of a hexadecimal string to be the number of non-zero coordinates. So (A, F, 1, 2, 0) has weight 4 and (1,2,0,0, F) has weight 3. Let hn,k be the number of n-digit hexadecimal strings with weight k. Choose one of the following questions to answer: You do not need to do both. 1. Find a recurrence relation for hn,k. Justify your answer. 2. Find a formula for hn,k. Justify your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 1 Let be a hexadecimal string with n-digits. In other words = (1,...,n) where each coor- dinate x is equal to one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Define the weight of a hexadecimal string to be the number of non-zero coordinates. So (A, F, 1, 2, 0) has weight 4 and (1,2,0,0, F) has weight 3. Let hn,k be the number of n-digit hexadecimal strings with weight k. Choose one of the following questions to answer: You do not need to do both. 1. Find a recurrence relation for hn,k. Justify your answer. 2. Find a formula for hn,k. Justify your answer.
Transcribed Image Text:Question 1 Let be a hexadecimal string with n-digits. In other words = (1,...,n) where each coor- dinate x is equal to one of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Define the weight of a hexadecimal string to be the number of non-zero coordinates. So (A, F, 1, 2, 0) has weight 4 and (1,2,0,0, F) has weight 3. Let hn,k be the number of n-digit hexadecimal strings with weight k. Choose one of the following questions to answer: You do not need to do both. 1. Find a recurrence relation for hn,k. Justify your answer. 2. Find a formula for hn,k. Justify your answer.
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