My homework problem invloves adding negative and positivebinary numbers. How do

Question

My homework problem invloves adding negative and positivebinary numbers. How do I determine how many bits to use torepresent a number and how do I solve this problem?

Perform the arithmetic operations (+33)+(-21) and (-37)-(-26) inbinary using signed 2’s complement representation fornegative numbers. Thank you. My homework problem invloves adding negative and positivebinary numbers. How do I determine how many bits to use torepresent a number and how do I solve this problem?

Perform the arithmetic operations (+33)+(-21) and (-37)-(-26) inbinary using signed 2’s complement representation fornegative numbers. Thank you. Thank you.

Explanation / Answer

In general, we can use 8 bit representation to denote numbersfrom 0 to 255, since we can represent the two bits 0 and 1 in 256(2 power 8 ) ways in 8 bit form.

Following is the way to solve the given expressions:

To represent a negative number we use 2’s complement.

So +21 is 00010101 and -21 is 2’s complement of 00010101(+21)

2’s complement of 00010101 --- 1’s complement +1

11101010

00000001

________

11101011

Now we add +33 (00100001) and -27 (11101011)

00010001

11101011

________

00001100 = 12

37 – 00100101 and – 37 is 2’s complement of37

11011010

00000001

________

11011011

26 – 00011010 and -26 is 2’s complement of 26

11100101

00000001

________

11100110

To subtract two numbers, we add the 2’s complement ofsecond number to the first number and again 2’s complementthe result to obtain the subtraction value.

So we take the 2’s complement of -26 and add it to-37

2’s complement of -26 is

00011001

00000001

________

00011010

Now we add this number to -37

11011011

00011010

________

11110101

2’s complement of the obtained value 11110101 is theresult.

2’s complement is

00001010

00000001

________

00001011 = 11

(-37)-(-26) =11             

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