7/17/2016 HW 13: Mod Arithmetic and ID numbers-Benny Jones Instructor: Thara Lowndes Course: Math 101 Summer 2016Sec. 953 (Choden) Student: Benny Jones Date: 7/17/16 Assignment: HW 13: Mod Arithmetic and ID numbers 1. Find the quotient and remainder in the division of n by m for: n = 84 and m = 13. The quotient is The remainder is 2. Find the quotient and remainder in the division of n by m for: n = 43 and m = 48. The quotient is The remainder is 3. Find the quotient and remainder in the division of n by m for: n = 201 and m = 14. The quotient is The remainder is 4. Is p q (mod m) for p = 56 , q = 12 , and m = 11 ? A. No, it is not. B. Yes, it is. 5. Is p q (mod m) for p = 85 , q = 31 , and m = 10 ? A. No, it is not. B. Yes, it is. 6. Is p q (mod m) for p = 14 , q = 54 , and m = 8 ? A. No, it is not. B. Yes, it is. 7. Perform the indicated calcuation in Zm . Write your answer in the form of [r] with 0 r < m for: [10 ] + [14 ] in Z15 The answer is . 8. Perform the indicated calcuation in Zm . Write your answer in the form of [r] with 0 r < m for: [7 ] + [12 ] in Z10 The answer is . https://xlitemprod.pearsoncmg.com/api/v1/print/math 1/2 7/17/2016 HW 13: Mod Arithmetic and ID numbers-Benny Jones 9. Perform the indicated calcuation in Zm . Write your answer in the form of [r] with 0 r < m for: [22 ] + [12 ] in Z8 The answer is . 10. The first nine digits of an ISBN is 2 534 81144. What is the correct check digit? The correct check digit is 11. The first nine digits of an ISBN is 0 454 59003. What is the correct check digit? The correct check digit is 12. The Universal Product Code (UPC) is a 12digit number found on products that enables them to be identified by electronic scanning devices. The first six digits identify the country of origin and the manufacturer, the next five digits indicate the product, and the last digit is a check digit. If the first eleven digits of a UPC are a1, a2 ,,,,,,a11 , then the check digit a12 is chosen so that 0 a12 < 10 and 3a1 + a2 + 3a3 + a4 + ...a12 0(mod10). Find the correct digit for the product code that has 0 20520 31546 as its first 11 digits. The correct check digit is 13. Federal Express packages carry a 10digit identification number n. Its last digit x is a check digit that equals the remainder in the division of (n x)/10 by 7. Find the last digit of the package tracking number with 906284625 as its first nine digits. The check digit is . 14. Perform the indicated calcuation in Zm . Write your answer in the form of [r] with 0 r < m for: [10 ] + [6 ] in Z12 The answer is . https://xlitemprod.pearsoncmg.com/api/v1/print/math 2/2 7/17/2016 HW 14: Binary codes (Section 7.2)-Benny Jones Instructor: Thara Lowndes Course: Math 101 -Summer 2016-Sec. 953 (Choden) Student: Benny Jones Date: 7/17/16 1. Assignment: HW 14: Binary codes (Section 7.2) Determine the parity check digit that should be appended so that the total number of I's is even for . The check digit should be 2. Determine the parity check digit that should be appended so that the total number of I's is even for . The check digit should be 3. Determine the parity check digit that should be appended so that the total number of I's is even for . The check digit should be 4. Determine the parity check digit that should be appended so that the total number of I's is even for . The check digit should be 5. Determine the Hamming distance between and c = 0111 The Hamming distance is 6. Determine the Hamming distance between and c = 01101 The Hamming distance is 7. Determine the Hamming distance between and c = 101000 The Hamming distance is 8. Determine the Hamming distance between and c = 01100010 The Hamming distance is 9. Add the given codewords using addition over The result is . in each place for and . . 11. Add the given codewords using addition over The result is and . 10. Add the given codewords using addition over The result is in each place for in each place for and . . 12. Suppose that a linear code has codewords { , the maximum number of errors that can be detected. , , , , , , }. Determine For this linear code, at most https://xlitemprod.pearsoncmg.com/api/v1/print/math error(s) can be detected. 1/1