Addition with eight bit 2's complement numbers. [Check my Work]

In summary, the concept of "Addition with eight bit 2's complement numbers" refers to a method of performing addition on binary numbers using eight bits and the 2's complement notation. This notation is commonly used in computer systems to represent negative numbers. To add two eight bit 2's complement numbers, one must add the numbers without considering the sign, handle overflow if necessary, and take the 2's complement if the numbers have different signs. The purpose of using 2's complement notation is to make it more efficient for computer systems to handle both positive and negative numbers. Common errors when adding eight bit 2's complement numbers include overflow and forgetting to take the 2's complement of a negative number. To check your work
  • #1
shamieh
539
0
Perform the following operations involving eight-bit 2's complement numbers and indicate whether arithmetic overflow occurs.

1) 01110101 + 11011110.

So I have a +Positive + a -Negative number. So I just added normally, and got the result of 01010011.

I realized before I started the problem I essentially had 117 +(-34) which is really 117 - 34 = 83.

So my result 01010011 = 83. Was there an easier way I could have done this? And, is this correct? It seems logically correct, but I've been known to screw these up. Also, there would be no overflow right?
 
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  • #2
Your calculation is correct. The operation results in a carry, but no overflow.
 

FAQ: Addition with eight bit 2's complement numbers. [Check my Work]

What is the concept of "Addition with eight bit 2's complement numbers"?

The concept of "Addition with eight bit 2's complement numbers" refers to a method of performing addition on binary numbers that are represented using eight bits and the 2's complement notation. This notation is commonly used in computer systems to represent negative numbers.

How do you add two eight bit 2's complement numbers?

To add two eight bit 2's complement numbers, follow these steps:

  • Add the two numbers without considering the sign (treat them as unsigned numbers).
  • If the result is greater than 255 (the maximum value of an eight bit number), subtract 256 from the result.
  • If the numbers being added have different signs, ignore the sign of the smaller number and take the 2's complement of the larger number. Then, add the two numbers using the first two steps.

What is the purpose of using 2's complement notation in addition with eight bit numbers?

2's complement notation allows for negative numbers to be represented using the same number of bits as positive numbers, making it more efficient for computer systems to handle both positive and negative numbers. Additionally, it simplifies subtraction operations, as subtracting a number is equivalent to adding its 2's complement.

What are some common errors that can occur when adding eight bit 2's complement numbers?

One common error is overflow, which occurs when the result of the addition is greater than 255. This can be avoided by using more bits to represent the numbers. Another error is forgetting to take the 2's complement of a negative number before adding it to a positive number with a different sign.

How can I check my work when adding eight bit 2's complement numbers?

To check your work, you can use a calculator or an online tool that performs addition with 2's complement numbers. Additionally, you can convert the numbers back to decimal form and verify that the result is correct.

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