Many common logical operations, like selecting and comparing, and the behavior of many simple mechanisms, like a light or a lock, can be expressed by truth values. Chapter 4, on punch-card mechanisms, contains a number of examples. * * * * * pronoun, variable In ordinary language, a _pronoun_, like “he,” “she,” “it,” “the former,” “the latter,” is a word that usually stands for a noun previously referred to. A pronoun usually stands for the last preceding noun that the grammar allows. In mathematics, a _variable_, like “_a_,” “_b_,” “_x_,” “_m₁_,” “_m₂_” closely resembles a pronoun in ordinary language. A variable is a symbol that usually stands for a number previously referred to, and usually it stands for the same number throughout a particular discussion. multiplicand, dividend, augend, etc. IN THE THE NAME THE NAME THE NAME EQUATION: OF _a_ IS: OF _b_ IS: OF _c_ IS: _a_ + _b_ = _c_ augend addend sum _a_ - _b_ = _c_ minuend subtrahend remainder _a_ × _b_ = _c_ multiplicand multiplier product _a_ ÷ _b_ = _c_ dividend divisor quotient _Augend_ and _addend_ are names of registers in the Harvard Mark II calculator (see Chapter 10). subtraction by adding, nines complement Two digits that add to 9 (0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and 5) are called _nines complements_ of each other. The _nines complement_ of a number _a_ is the number _b_ in which each digit of _b_ is the nines complement of the corresponding digit of _a_; for example, the nines complement of 173 is 826. Ordinary subtraction is the same as addition as of the nines complement, with a simple correction; for example, 562 less 173 (equal to 389) is the same as 562 plus 826 (equal to 1388) less 1000 plus 1. end-around-carry The correction “less 1000 plus 1” of the foregoing example may be thought of as carrying the 1 (in the result 1388) around from the left-hand end to the right-hand end, where it is there added. So the 1 is called _end-around-carry_. tens complement Two digits that add to 10 are called _tens complements_ of each other. The _tens complement_ of a number _a_, however, is equal to the nines complement of the number plus 1. For example, the tens complement of 173 is 827. When subtracting by adding a tens complement, the left-most digit 1 in the result is dropped. For example, 562 less 173 (equal to 389) is the same as 562 plus 827 (equal to 1389) less 1000. power, square, cube, reciprocal, etc.