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1. Add the following binary numbers.

a. 1110110 + 111011

b. 1111011+11011

C. 010111111111

II. Subtract the following binary numbers.

a. 1010110-11011

b. 1101011-1011

c. 001101111-11111

 

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Solution:

1. Add the following binary numbers:

a. 1110110 + 111011

To add binary numbers, we start from the rightmost digits and move towards the left, carrying over any excess 1s.

   1110110
 +  111011
_________
  10100101

Therefore, 1110110 + 111011 = 10100101 in binary.

b. 1111011 + 11011

   1111011
 +   11011
_________
  10010110

Therefore, 1111011 + 11011 = 10010110 in binary.

c. 010111111111

Since this is a single binary number, no addition is needed.

Therefore, 010111111111 remains the same.

II. Subtract the following binary numbers:

a. 1010110 - 11011

To subtract binary numbers, we start from the rightmost digits and move towards the left. If the digit being subtracted is greater than the digit being subtracted from, we borrow 1 from the next higher digit.

    1010110
 -    11011
_________
    1000101

Therefore, 1010110 - 11011 = 1000101 in binary.

b. 1101011 - 1011

    1101011
 -    1011
_________
    1100000

Therefore, 1101011 - 1011 = 1100000 in binary.

c. 001101111 - 11111

   001101111
 -     11111
___________
   001010000

Therefore, 001101111 - 11111 = 001010000 in binary.