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

## 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.
Answer:
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...
\$45.00 for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Discrete Math Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

SUBMIT YOUR HOMEWORK
We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

• 1
• 2
• 3
Live Chats