C and Java have six relational operators
(==
, !=
,
<
, <=
,
>
, >=
)
and four logical operators
(&&
, 
, !
,
? :
).
In Java all of these return booleans, true
or false
.
In C and C++, these operators return an integer, 1 for true
and 0 for false.
When evaluating logical operators, C considers any nonzero value to be
true. This means that all of the following expressions have the value
1 in C and C++.
5 && 6
0  1000000
! 0
1 < 2 < 3
5 ? 1: 3
The MIPS32 architecture has a four instructions,
SLT
, SLTI
, SLTIU
, and SLTU
,
that can be used to implement the <
operator.
However, most compilers will use branch instructions,
which resemble the if
, when
implementing the relational and logical operators.
Evaluation of relational operators
In hardware the test of x <y is usually accomplished by subtracting y from x and testing if the result is less than 0. The table below illustrates how this transformation is made for the six relational operators.
x == y 
xy == 0 
x != y 
xy != 0 
x < y 
xy < 0 
x <= y 
xy <= 0 
x > y 
xy > 0 
x >= y 
xy >= 0 
As you will see in a few days, rarely does the C compiler actually store the result of relational operator because programmers just don’t do that very often (or don’t do that as often as they should). But suppose an assignment like the following does appear in a program.
τ = x != y ;
Most likely it would be implemented by something similar to the following C code.
τ = 0 ; if (x  y != 0) { τ = 1 ; }
Evaluation of logical operators
The logical not operator of C is easy.
It can be implemented with a relational
operator. Every instance of !τ
can be transformed to τ!=0
.
The other three logical operator of C (and Java)
are short
circuit operators.
They may not evaluate all of their
operands before yielding a result.
These operators are &&
, 
,
and the ? :
ternary operator.
They can be implemented using C’s if
construct
using
the control structure rules
if they are first translated into if
–else
statements.
The following table shows the translation rules for
these logical operators.
Study them to make sure you see where the short cut is taken.
τ = exp1 && exp2 ; 

τ = exp1  exp2 ; 
if (exp1) τ = 1 ; else if (exp2) τ = 1 ; else τ = 0 ; 
τ = exp1 ? exp2 : exp3 ; 

Also, make sure you understand why the short circuit is needed in a Java expression like the following:
done = x < 0  x >= A.length()  A[x] < 0 ;