Compute a logical right shift AB in Java where A and B are i

Compute a logical right shift (A>>>B) in Java where A and B are ints, and (A>>B) in C++ where A and B are unsigned ints.

Convert the following base 10 numbers to 16-bit two’s complement. Show your work.

Solution

A = 1111 0000 0000 0000 0000 0000 1100 0011 0000

B = 0000 0000 0000 0000 0000 0000 0000 0000 0101

In JAVA

In JAVA >>> is treated as unsigned right shift   

This operator shifts each bits of A , B number of times towards right. And at each shift the MSB of A is set to 0.

So here B=5

A= 1 111 0000 0000 0000 0000 0000 1100 0011 0000

As sign bit is 1, so A is a negative number. So represent it in 2’s complement form,

2’s complement of A=          1’s complements of A +1

I,e =             1 000 1111 1111 1111 1111 1111 0011 1101 0000

Now after 1^st shift: 0 100 0111 1111 1111 1111 1111 1001 1110 1000

After 2^nd shift       : 0 010 0011 1111 1111 1111 1111 1100 1111 0100

After 3rd shift      :              0 001 0001 1111 1111 1111 1111 1110 0111 1010

After 4th shift      :              0 000 1000 1111 1111 1111 1111 1111 0011 1101

After 5th shift      :              0 000 0100 0111 1111 1111 1111 1111 1001 1110

Now A =                                              0 000 0100 0111 1111 1111 1111 1111 1001 1110 (ans)

As sign bit is 0 .It is a positive number . value remains same

In C++

In C++ >> is treated as signed right shift

This operator shifts each bits of A , B number of times towards right. And at each shift the MSB of A is set to 0 if the number is +ve and 1 if the number is negative.

So here B=5

A= 1 111 0000 0000 0000 0000 0000 1100 0011 0000

As sign bit is 1, so A is a negative number. So represent it in 2’s complement form,

2’s complement of A=          1’s complements of A +1

I,e       

=             1 000 1111 1111 1111 1111 1111 0011 1101 0000

Now after 1^st shift :   1 100 0111 1111 1111 1111 1111 1001 1110 1000

After 2^nd shift       :              1 110 0011 1111 1111 1111 1111 1100 1111 0100

After 3rd shift      :              1 111 0001 1111 1111 1111 1111 1110 0111 1010

After 4th shift      :              1 111 1000 1111 1111 1111 1111 1111 0011 1101

After 5th shift      :              1 111 1100 0111 1111 1111 1111 1111 1001 1110

Now A =                                              1 111 1100 0111 1111 1111 1111 1111 1001 1110

As sign bit is 1 .It is a negative number , To find actual value, find 2’s complement of above

I,e                                            1 000   0011 1000 0000 0000 0000 0000 0110 0001

                                         +     0 000   0000 0000 0000 0000 0000 0000 0000 0001

                                                ----------------------------------------------------------------------        

                                    =          1 000   0011 1000 0000 0000 0000 0000 0110 0010 (ans)

-------------------------------------------------------------------------------------------------------------------------------------------

Convert (121)₁₀ to 16 bit 2’s complement

2’s complement of a number = 1’s complement of that number + 1

121                                         : 0 000   0000       0111       1001                       // bold and underlined bit is sign bit

1’s Complement : 0 111   1111       1000       0110

                                                + 1

                                                ---------- ----------------------------

2’s Complement : 0 111 1111    1000    0111 (ans)

------------------------------------------------------------------------------------------------------------------------------------------

Convert (-99)₁₀ to 16 bit 2’s complement

-99                                          : 1 000   0000       0110       0011                       // bold and underlined bit is sign bit

1’s Complement : 1 111   1111       1001       1100

                                                + 1

                                                ---------- ----------------------------

2’s Complement : 1 111   1111       1001       1101 (Ans)