Cannot solve mips with and, or, and xor operators

Question

I am stuck on this problem and need help. I have two registers

$t2 which is 00000000 00000000 00000000 01111001

and

$t3 which is 11111111 11111111 11111111 11100011

the three questions that are being asked are (answers must be in binary)

and $s2,$t2,$t3

or $s2,$t2,$t3

xor $s2,$t2,$t3

I have looked everywhere online and in my textbook but I cannot for the life of me find out what these operators do. I am not asking for the answers but just for some guidance on how I should start working on these problems.

Thanks.

Answer 1

These are bitwise operators. They derive their names form the logic gates/boolean math operators that they implement:

AND => both inputs true (1) generates true
OR  => any input true generates true
XOR => true only if one input is true and the other is false

See the wikipedia articles for more info on the operators:

• http://en.wikipedia.org/wiki/AND_gate
• http://en.wikipedia.org/wiki/OR_gate
• http://en.wikipedia.org/wiki/XOR_gate

Because these are very basic boolean operators/logic gates, it is often assumed in books/text concerning CPU design and assembly programming that the reader is familiar with them. An assumption that perhaps shouldn't be made since programming is nowdays a more wide discipline encompassing everything from biologists to stock market analyst to engineers.

When it comes to applying the operator on a string of bits such as a word or a byte all the bits in the two inputs are processed in parallel. For example, let's AND two bytes:

input 1 = 11110000
input 2 = 00111100
------------------
output  = 00110000
            ▲▲
            ││
            └┴──────── true because both bits from
                       input 1 and input 2 are true
                       (see difinition of AND)

The same works with the other operators.