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3 years ago

Drag each label to the correct location on the image.

Computers and Technology

1 answer:

expeople1 [14]3 years ago

6 0

Answer:

Black is the absence of all light. Things appear black when they do not reflect or emit light. White is the presence of all colors of visible light. Objects appear white when they reflect or emit all wavelengths of visible light (or at least three wavelengths - Red, Blue and Green - in equal intensity).

Explanation:

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Add the following 2's complement binary numbers. Also express the answer in decimal. a. 01+ 1011b. 11+ 01010101c. 0101+ 110d. 01

kenny6666 [7]

Answer:

(a) 01 + 1011

Convert the two numbers into their 4-bit representation.

=> 01 = 0001

=> 1011

Addition of the two numbers (in their 2's complement form) gives the following:

0 0 0 1 ------------------> + 1 (in decimal)

1 0 1 1 ------------------> - 5 (in decimal)

1 1 0 0 -------------------> - 4 (in decimal)

Explanation for (a)

01 or 0001

Since the most significant bit is 0 (leftmost bit), it shows that it is a positive number. Therefore, it can be directly converted to its decimal representation as follows:

0001 = 0 x $2^{3}$ + 0 x $2^{2}$ + 0 x $2^{1}$ + 1 x $2^{0}$ = 1

0001 is + 1 in decimal.

1011

Its most significant bit(MSB) is 1 showing that it is negative.

Flipping all its bits and adding 1 to the result, will convert it to it's positive counterpart.

i.e 1011 => 0100 + 1 = 0101.

Converting the result (0101) to decimal gives

0101 = 0 x $2^{3}$ + 1 x $2^{2}$ + 0 x $2^{1}$ + 1 x $2^{0}$ = 5

1011 is -5 in decimal

01 + 1011 or 0001+ 1011 = 1100

The result (1100), of the addition of the two numbers, is a negative number as the MSB is 1.

Convert it to it's positive counterpart.

i.e 1100 => 0011 + 1 = 0100.

Converting the result (0100) to decimal gives

0100 = 0 x $2^{3}$ + 1 x $2^{2}$ + 0 x $2^{1}$ + 0 x $2^{0}$ = 4

Therefore, the result, 1100 is -4 in decimal.

===================================================

(b) 11 + 01010101

Convert the two numbers into their 8-bit representation since one of them is in 8-bit.

PS: Taking 11, its MSB is 1 showing that it is a negative number. Also, it's 8-bit representation will mean pre-padding it with ones(1s) rather than zeros as follows. In other words, pre-padding a 2's complement number is done using its sign bit.

=> 11 = 11111111

=> 01010101

Addition of the two numbers (in their 2's complement form) gives the following:

1 1 1 1 1 1 1 1 ------------------> - 1 (in decimal)

0 1 0 1 0 1 0 1 ------------------> + 85 (in decimal)

1 0 1 0 1 0 1 0 0 -------------------> + 84 (in decimal)

Discard the carry-out bit (1) making the result 01010100

Explanation for (b)

11 or 11111111

Its MSB is 1 showing that it is negative.

Convert it to it's positive counterpart.

11111111 => 00000000 + 1 = 00000001

Converting the result (00000001) to decimal gives 1

11 or 11111111 is - 1 in decimal.

01010101

Its MSB is 0 showing that it is also positive. Now, convert to decimal

01010101 = 85

01010101 is + 85 in decimal.

11111111 + 01010101 = 01010100

The result (01010100), is also positive as the MSB is 0. Now, convert to decimal.

01010100 = 84

Therefore the result (01010100) is + 84 in decimal.

===================================================

Convert the two numbers into their 4-bit representations.

=> 0101 = 0101

=> 110 = 1110

Addition of the two numbers (in their 2's complement form) gives the following:

0 1 0 1 ------------------> + 5 (in decimal)

1 1 1 0 -----------------> - 2 (in decimal)

1 0 0 1 1 -------------------> + 3 (in decimal)

Dicard the carry-out bit (leftmost bit) to get 0011 as result.

Explanation for (c)

0101

Since the MSB is 0 (leftmost bit), it shows that it is a positive number. Now, convert to decimal.

0101 = 5

0101 is +5 in decimal.

110 or 1110

Its MSB is 1 showing that it is negative.

Convert it to it's positive counterpart.

i.e 1110 => 0001 + 1 = 0010.

Converting the result (0010) to decimal gives

0010 = 2

1110 is -2 in decimal

0101 + 110 = 0101+ 1110 = 0011

The result (0011), is a positive number as the MSB is 0.

Converting the result (0011) to decimal gives

0011 = 3

Therefore, the result, 0011 is 3 in decimal.

===================================================

(d) 01 + 10

Convert the two numbers into their 4-bit representation.

=> 01 = 0001

=> 10 = 1110

Addition of the two numbers (in their 2's complement form) gives the following:

0 0 0 1 ------------------> + 1 (in decimal)

1 1 1 0 ------------------> - 2 (in decimal)

1 1 1 1 -------------------> - 1 (in decimal)

Explanation for (d)

01 or 0001

Since the MSB is 0 (leftmost bit), it shows that it is a positive number. Now convert to decimal.

0001 = 1

0001 is + 1 in decimal.

1110

Its MSB is 1 showing that it is negative.

Convert it to it's positive counterpart.

i.e 1110 => 0001 + 1 = 0010.

Converting the result (0010) to decimal gives

0010 = 2

1110 is -2 in decimal

01 + 1011 or 0001+ 1110 = 1111

The result (1111), is a negative number as the MSB is 1.

Convert it to it's positive counterpart.

i.e 1111 => 0000 + 1 = 0001.

Converting the result (0001) to decimal gives

0001 = 1

Therefore, the result, 1111 is -1 in decimal.

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