1.3: The Control Bit

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Page ID: 50152

Paul Penfield, Jr.
Massachusetts Institute of Technology via MIT OpenCourseWare

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In computer programs, Boolean expressions are often used to determine the flow of control, i.e., which statements are executed. Suppose, for example, that if one variable \(x\) is negative and another \(y\) is positive, then a third variable \(z\) should be set to zero. In the language Scheme, the following statement would accomplish this: (if (and (< x 0) (> y 0)) (define z 0)) (other languages have their own ways of expressing the same thing).

The algebra of control bits is like Boolean algebra with an interesting difference: any part of the control expression that does not affect the result may be ignored. In the case above (assuming the arguments of and are evaluated left to right), if \(x\) is found to be positive then the result of the and operation is 0 regardless of the value of \(y\), so there is no need to see if \(y\) is positive or even to evaluate \(y\). As a result the program can run faster, and side effects associated with evaluating \(y\) do not happen.