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Let A= 1100 1010 and B= 0000 0100 be two 8-bit 2's complement numbers. Their product in 2's complement is
- a)1100 0100
- b)1001 1100
- c)1010 0101
- d)0010 1000
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let A= 1100 1010 and B= 0000 0100 be two 8-bit 2s complement numbers. ...
A= 1100 1010, since MSB=1 hence the number is negative.
2’s complement of A= 00110110
A= -54
B= 0000 0100
B= 4 (Since the number is positive so there is no 2’s complement).
Now product of A*B= -54*4 = 216.
Binary representation of -216= 1101 1000.
2’scomplement of -216= 0010 1000.
Most Upvoted Answer
Let A= 1100 1010 and B= 0000 0100 be two 8-bit 2s complement numbers. ...
To find the product of two 8-bit 2's complement numbers A and B, we need to perform binary multiplication. Let's break down the process step by step.
Step 1: Convert the given numbers A and B into their decimal equivalents.
A = 1100 1010 (2's complement) = -54 (decimal)
B = 0000 0100 (2's complement) = 4 (decimal)
Step 2: Perform binary multiplication.
We multiply A and B as we would with regular binary numbers. However, since A and B are in 2's complement form, we need to consider the sign bit separately.
```
1100 1010 (A)
x 0000 0100 (B)
_______________
0000 1010 (Partial product: A * 0)
+ 0000 0000 (Partial product: A * 0 shifted one place to the left)
+ 1100 1010 (Partial product: A * 1 shifted two places to the left)
+ 0000 0000 (Partial product: A * 0 shifted three places to the left)
________________
= 0010 1000 (Result of binary multiplication)
```
Step 3: Convert the result back into 2's complement form.
The result of binary multiplication is 0010 1000. Since we are working with 8-bit numbers, we need to consider the most significant bit, which is 0. Therefore, the result is positive.
Step 4: Convert the result into its decimal equivalent.
0010 1000 (2's complement) = 40 (decimal)
Thus, the product of A and B in 2's complement form is 0010 1000, which corresponds to option 'D' in the given options.
Step 1: Convert the given numbers A and B into their decimal equivalents.
A = 1100 1010 (2's complement) = -54 (decimal)
B = 0000 0100 (2's complement) = 4 (decimal)
Step 2: Perform binary multiplication.
We multiply A and B as we would with regular binary numbers. However, since A and B are in 2's complement form, we need to consider the sign bit separately.
```
1100 1010 (A)
x 0000 0100 (B)
_______________
0000 1010 (Partial product: A * 0)
+ 0000 0000 (Partial product: A * 0 shifted one place to the left)
+ 1100 1010 (Partial product: A * 1 shifted two places to the left)
+ 0000 0000 (Partial product: A * 0 shifted three places to the left)
________________
= 0010 1000 (Result of binary multiplication)
```
Step 3: Convert the result back into 2's complement form.
The result of binary multiplication is 0010 1000. Since we are working with 8-bit numbers, we need to consider the most significant bit, which is 0. Therefore, the result is positive.
Step 4: Convert the result into its decimal equivalent.
0010 1000 (2's complement) = 40 (decimal)
Thus, the product of A and B in 2's complement form is 0010 1000, which corresponds to option 'D' in the given options.
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Let A= 1100 1010 and B= 0000 0100 be two 8-bit 2s complement numbers. Their product in 2s complement isa)1100 0100b)1001 1100c)1010 0101d)0010 1000Correct answer is option 'D'. Can you explain this answer?
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