Question

Consider the numbers M = 1041 and N = 1165, both in base 10. Write them in baser, and perform M - N using the (r - 1)'s complement representation subtraction algorithm for: (i) = 2 M2 N2: (M - N)2: (ii) = = 8 Mg: Ng: (M - N)8: b) Consider the base-9 number 7654329. Write the number in the r's complement representation, that is in the 9's complement representation, since r = 9. c) Knowing that we have the equality: 424(3-2) = 24A(2+1) determine the value of .

Answer 1

To perform (M - N) in base 2, find the (r - 1)'s complement of N, add M to the complement of N, and discard any carry from the leftmost bit. In base 8, subtract N from M. The 9's complement representation of the base-9 number 7654329 is obtained by replacing each digit with (9 - digit). A in the equation 424(3-2) = 24A(2+1) is equal to 4.

Step-by-step explanation:

In base 2, M = 1041 is equal to 10000001101 and N = 1165 is equal to 10010001101. To perform (M - N) in base 2, we use the (r - 1)'s complement representation subtraction algorithm. First, find the (r - 1)'s complement of N by replacing each 0 with a 1 and each 1 with a 0. Then add 1 to the result. Now, add M to the complement of N, discarding any carry from the leftmost bit to get the final result.

In base 8, M = 1041 is equal to 2011 and N = 1165 is equal to 2165. To perform (M - N) in base 8, we subtract N from M as usual.

In the base-9 number 7654329, the 9's complement representation is obtained by replacing each digit with (9 - digit). For example, 7 becomes 2, 6 becomes 3, and so on. This gives us the number 2345670 in the 9's complement representation.

To determine the value of A in the equation 424(3-2) = 24A(2+1), we can simplify the equation. The left-hand side becomes 424 = 24A. Equating the corresponding digits, we have 4 = A. Therefore, A = 4.