tYSR20

56 Part I: Introduction to C++ ProgrammingRoman numeral expressionsOn a historical note, I should mention that somenumbering systems actually hinder computations.The Roman numeral system is a (so tospeak) classic example that greatly hinderedthe development of math.Adding two Roman numerals isn’t too difficult:XIX + XXVI = XLVThink this one out:a) IX + VI: The I after the V cancels out the Ibefore the X so the result is V carry the X.b) X + XX: Plus the carry X is XXXX, which isexpressed as XL.Subtraction is only slightly more difficult.Ah, but multiplying two Roman numerals all butrequires a bachelor’s degree in mathematics.(You end up with rules like X promotes the digitson the right by 1 letter so that X –* IV becomesXL.) Division practically required a Ph.D., andhigher operations such as integration wouldhave been completely impossible.Love those Arabic numerals . . .Performing Bitwise Logical OperationsAll C++ numbers can be expressed in binary form. Binary numbers use onlythe digits 1 and 0 to represent a value. The following Table 4-2 defines the setof operations that work on numbers one bit at a time, hence the term bitwiseoperators.Table 4-2OperatorFunctionBitwise Operators~ NOT: Toggle each bit from 1 to 0 and from 0 to 1&AND each bit of the left-hand argument with that on the right| OR each bit of the left-hand argument with that on the right^XOR (exclusive OR) each bit of the left-hand argument with that onthe rightBitwise operations can potentially store a lot of information in a small amountof memory. There are a lot of traits in the world that have only two (or, atmost, four) possibilities — that are either this way or that way. You are eithermarried or you’re not (you might be divorced but you are still not currently