1-9In addition,X + Y = ZIn subtraction, the reverse is true; that is,Z – Y = XORZ – X = YThus, in subtraction the minuend is always found in array Z and the subtrahend in either row X orcolumn Y. If the subtrahend is in row X, then the remainder will be in column Y. Conversely, if thesubtrahend is in column Y, then the difference will be in row X. For example, to subtract 8 from 15, find8 in either the X row or Y column. Find where this row or column intersects with a value of 15 for Z; thenmove to the remaining row or column to find the difference.THE BINARY NUMBER SYSTEMThe simplest possible number system is the BINARY, or base 2, system. You will be able to use theinformation just covered about the decimal system to easily relate the same terms to the binary system.Unit and NumberThe base, or radixyou should remember from our decimal sectionis the number of symbols usedin the number system. Since this is the base 2 system, only two symbols, 0 and 1, are used. The base isindicated by a subscript, as shown in the following example:1_{2}When you are working with the decimal system, you normally don't use the subscript. Now that youwill be working with number systems other than the decimal system, it is important that you use thesubscript so that you are sure of the system being referred to. Consider the following two numbers:11 11With no subscript you would assume both values were the same. If you add subscripts to indicatetheir base system, as shown below, then their values are quite different:11_{10 }11_{2}The base ten number 11_{10} is eleven, but the base two number 11_{2} is only equal to three in base ten.There will be occasions when more than one number system will be discussed at the same time, so youMUST use the proper Subscript.Positional NotationAs in the decimal number system, the principle of positional notation applies to the binary numbersystem. You should recall that the decimal system uses powers of 10 to determine the value of a position.The binary system uses powers of 2 to determine the value of a position. A bar graph showing thepositions and the powers of the base is shown below:

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