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Compute the following binaryarithmetic operations using 2’s complement method. Show all the steps clearly. (LO 01)(2*5 = 10 Marks)a) Sum of -30 and 17b) Sum of -42 and -15c) Sum of -13 and -16

Question

Compute the following binaryarithmetic operations using 2’s complement method. Show all the steps clearly. (LO 01)(2*5 = 10 Marks)a) Sum of -30 and 17b) Sum of -42 and -15c) Sum of -13 and -16

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Solution

a) Sum of -30 and 17

Step 1: Convert the numbers to binary -30 in binary is 11110 (2's complement of 30 which is 00010) 17 in binary is 10001

Step 2: Add the binary numbers 11110 +10001

101111

Step 3: Since the result is a negative number (starts with 1), take the 2's complement to get the final result 2's complement of 101111 is 010001, which is -13 in decimal.

b) Sum of -42 and -15

Step 1: Convert the numbers to binary -42 in binary is 101010 (2's complement of 42 which is 010110) -15 in binary is 1111 (2's complement of 15 which is 0001)

Step 2: Add the binary numbers 101010

  • 1111

110101

Step 3: Since the result is a negative number (starts with 1), take the 2's complement to get the final result 2's complement of 110101 is 001011, which is -57 in decimal.

c) Sum of -13 and -16

Step 1: Convert the numbers to binary -13 in binary is 1101 (2's complement of 13 which is 0011) -16 in binary is 10000 (2's complement of 16 which is 0000)

Step 2: Add the binary numbers 1101 +10000

11101

Step 3: Since the result is a negative number (starts with 1), take the 2's complement to get the final result 2's complement of 11101 is 00011, which is -29 in decimal.

This problem has been solved

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