 Discrete Math Interesting Exercises - Base Conversion, RSA, Linear Congruences, Transposition Cipher

Subject Computer Science Discrete Math

Question

P1. Convert (7206)8 and (AOEB)16 to binary.

P2. Express gcd(84, 119) as a linear combination of 84 and 119.

P3. Use the Chinese Remainder Theorem to solve the following system of linear congruences: x ≡ 1 mod 4 x ≡ 2 mod 5 x ≡ 3 mod 7

P4. Encrypt the message GRIZZLY BEARS using blocks of five letters and the transposition cipher based on the permutation of {1,2,3,4,5} with σ(1) = 3, σ(2)=5, σ(3)=1, σ(4) = 2 and σ(5)=4. For this problem, use the letter X as many times as necessary to fill out the final block of fewer than 5 letters.

P5. A check digit a13 for an ISBN-13 with initial digits a1, a2, …, a12 is determined by the congruence {(a1 + a3 +….+ a13) + 3(a2 + a4 + … +a12)} ≡ 0 mod 10. Determine if each of the following 13‐digit numbers is a valid ISBN‐13. a. 978‐0‐073‐20679-1 b. 978‐0-201‐10179‐9

P6. Determine the plaintext for the RSA ciphertext 2169 0628 5540 2169 6560 6401 4829 with n = 7747 (p = 61 and q = 127) and e=17.

Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

P1. Convert (7206)8 and (AOEB)16 to binary.
We first convert the number from octal to decimal and then to binary.
(7206)8=7*8^3+2*8^2+0*8+6=7*512+2*64+6=3,584+134=3,718
Now we transform the decimal number into binary.
3,718:2=1,859 remainder 0
1,859:2= 929 remainder 1
929:2=464 remainder 1
464:2=232 remainder 0
232:2=116 remainder 0...

This is only a preview of the solution. Please use the purchase button to see the entire solution

Related Homework Solutions

Discrete Mathematics Problem \$10.00
Discrete Mathematics
Division Algorithm
Computer Science
Primes
Proof
Integers
Discrete Math Questions \$40.00
Discrete Mathematics
Probability
Statistics
Combinations
Permutations
Outcomes
Balls
Replacements
Lists
Dices
Events
Digits
Integers
Odd Numbers
Even Numbers
Rows
Multiplication
Graph Exercises and Graph Representations \$13.00
Graph
Matrix
List
Vertices
Node
Edge
Representation
Undirected
Computer
Science
Discrete Math Exercises with Functions \$10.00
Function
Domain
Range
Solution
One-to-one
Onto
Set
Target
Equation
Codomain
Computer Science
Discrete Math
Induction Proof Exercises \$25.00
induction
proof
integer
relationship
polygon
triangles
triangulation
prove
discrete
math
Discrete Math Questions with Sets, Functions, Fibonacci, and Base Conversion \$35.00
Set
Interval
Base
Function
Fibonacci
Integer
One-to-one
Onto
Fraction
Real
Decimal
Point
Intersection
Union
Power
Cartesian
Product
Inverse
Injective
Element
Method
Bare
Hand
Induction
Live Chats