Given the following 8-bit integer binary variables: X1 = 11000110X2 = 11110111 What is the value in X3 after the following command? ADD X3, X2, X1

First, let's convert the binary numbers to decimal to make the addition easier.

X1 = 11000110 = 198 in decimal X2 = 11110111 = 247 in decimal

The ADD command adds X2 and X1 and stores the result in X3. So,

X3 = X2 + X1 X3 = 247 + 198 X3 = 445

However, since we're dealing with 8-bit integers, the range of values we can represent is from 0 to 255. If a calculation results in a number outside this range, it will "wrap around" from the start or end of this range. This is known as overflow.

So, to find the value that X3 would actually hold, we subtract the maximum value (255) plus 1 from the result:

X3 = 445 - (255 + 1) X3 = 445 - 256 X3 = 189

So, X3 would hold the value 189. To convert this back to binary:

X3 = 189 = 10111101 in binary.

To solve this problem, we first need to convert the binary numbers to decimal, add them, and then convert the result back to binary.

Step 1: Convert X1 and X2 from binary to decimal. X1 = 11000110 = 12^7 + 12^6 + 02^5 + 02^4 + 02^3 + 12^2 + 12^1 + 02^0 = 128 + 64 + 4 + 2 = 198 X2 = 11110111 = 12^7 + 12^6 + 12^5 + 12^4 + 02^3 + 12^2 + 12^1 + 12^0 = 128 + 64 + 32 + 16 + 4 + 2 + 1 = 247

Step 2: Add the decimal values of X1 and X2. 198 + 247 = 445

Step 3: Convert the result back to binary. 445 = 12^8 + 12^7 + 02^6 + 12^5 + 12^4 + 12^3 + 02^2 + 12^1 + 0*2^0 = 110111101

So, X3 = 110111101. However, since we are dealing with 8-bit integers, the result should be truncated to fit into 8 bits. Therefore, the final value of X3 is 01111101.