For the binary numbers X = 101011.1 and the number Y = 1100.1, assume the calcul

Question

For the binary numbers X = 101011.1 and the number Y = 1100.1, assume the calculator will fix the representation to 7 bits for integer and one bit for the fraction Which of the statements below are correct? -Y=1110011.0 in One's Complement -Y=1001100.11 in sign-magnitude notation -Y=1110011.1 in Two's complement X-Y=10011111.0 using two's complement method -x=1101011.1 in sign-magnitude notation -Y=0011.0 in One's complement -Y=10011.11 in Two'a complement X-Y=0011111.0 using two's complement method -Y=-1100.1 in sign-magnitude notation X-Y=11111.0 using two's complement method -X =-101011.1 in sign-magnitude notation

Explanation / Answer

The binary numbers are:

X = 101011.1

Y = 1100.1

-X = 1101011.1

- Y = 11100.1

The most significant bit 1 means a negative number

Concept of subtracting binary numbers rely on the fact that subtraction = adding a negative subtrahend

For example: 4 -3 = 4 + (-3) = 1

1.

When Y = 1100.1, the one’s compliment of Y will swap 1 to 0 and 0 to 1

1’s of Y = 0011.0

then –Y in 1s compliment = 10011.0

hence the first one is not correct

2. Sign magnitude notation of Y

3. 2’s compliment of -Y  

2’s compliment (2’s) = 1’s compliment + 1

1’s of Y = 0011.0

2’s of Y = 0011.0 + 1.0 = 0100.0

but for –Y put a one in the front

hence 2’s of –Y = 10100.0

hence Question 3 is not correct as well

4. X – Y = 101011.1 - 1100.1 = 11111.0

Selecting all true (= correct) statements:

5.

6.

–Y in 1s compliment = 10011.0

hence Q6 is not correct

7.

2’s of –Y = 10100.0

hence 7th is not correct

The binary numbers are:

X = 101011.1

Y = 1100.1

-X = 1101011.1

- Y = 11100.1

The most significant bit 1 means a negative number

Concept of subtracting binary numbers rely on the fact that subtraction = adding a negative subtrahend

For example: 4 -3 = 4 + (-3) = 1

1.

When Y = 1100.1, the one’s compliment of Y will swap 1 to 0 and 0 to 1

1’s of Y = 0011.0

then –Y in 1s compliment = 10011.0

hence the first one is not correct

2. Sign magnitude notation of Y

  

Selecting all true (= correct) statements:

The binary numbers are:

X = 101011.1

Y = 1100.1

-X = 1101011.1

- Y = 11100.1

The most significant bit 1 means a negative number

Concept of subtracting binary numbers rely on the fact that subtraction = adding a negative subtrahend

For example: 4 -3 = 4 + (-3) = 1

1.

When Y = 1100.1, the one’s compliment of Y will swap 1 to 0 and 0 to 1

1’s of Y = 0011.0

then –Y in 1s compliment = 10011.0

hence the first one is not correct

2. Sign magnitude notation of Y

3. 2’s compliment of -Y  

2’s compliment (2’s) = 1’s compliment + 1

1’s of Y = 0011.0

2’s of Y = 0011.0 + 1.0 = 0100.0

but for –Y put a one in the front

hence 2’s of –Y = 10100.0

Selecting all true (= correct) statements:

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