Computer Organization and Programming What is the sum of each pair of binary int

Question

Computer Organization and Programming

What is the sum of each pair of binary integers? (assuming 8-bit register is used) 10101111 + 11011011 10010111 + 11111111 Calculate the following operations using two's complement method: (assuming 4-bit register is used) 4 - 7 -3 - 6 What is the binary representation of the following hexadecimal numbers? 0126F9D4 6ACDFA95 What is the 16-bit hexadecimal representation of each of the following signed decimal integers? -21 -45 What is the decimal representation of each of the following signed binary numbers? 10110101 6 00101010 11110000 What is the sum of each pair of hexadecimal integers? 7C4 + 3 BE B69 + 7AD Assume there is a Mac and a HP computer each has an Intel microprocessor. Would an assembly program produced using the Mac computer run on the HP computer? Justify your answer.

Explanation / Answer

1. Sum of each pair of binary integers:

a. 1010 1111 + 1101 1011 = 1)1001 1010. Here the MSB 1 is a carry. And therefore, the result is: 1001 1010.

b. 1001 0111 + 1111 1111 = 1)1001 0110. Here the MSB 1 is a carry. And therefore, the result is: 1001 0110.

2. 2's complement summation:

a. 4 - 7:

4: 0100.

-7: -0111 = 1001 is the 2's complement representation of -7.

Now adding 4, and -7: 0100 + 1001 = 1101. As the result is a negative number, 2's complement of the result is: 0011 i.e., -3 is the answer.

b. -3 - 6:

-3: -0011 = 1101 is the 2's complement representation of -3.

-6: -0110 = 1010 is the 2's complement representation of -6.

Now adding -3, and -6: 1101 + 1010 = 1)0111. Here 1 is a carry. Dropping that, the result is: 0111. This actually gives an improper result, as the result -9 cannot be hold in just 4 bits.

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