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Carry and Borrow Principles - Continued | Up
Neets Module 13-Introduction to Number Systems and Logic Circuits | Next
Positional Notation - Continued |
1-9
In addition,
X + Y = Z
In subtraction, the reverse is true; that is,
Z – Y = X
OR
Z – X = Y
Thus, in subtraction the minuend is always found in array Z and the subtrahend in either row X or
column Y. If the subtrahend is in row X, then the remainder will be in column Y. Conversely, if the
subtrahend is in column Y, then the difference will be in row X. For example, to subtract 8 from 15, find
8 in either the X row or Y column. Find where this row or column intersects with a value of 15 for Z; then
move to the remaining row or column to find the difference.
THE BINARY NUMBER SYSTEM
The simplest possible number system is the BINARY, or base 2, system. You will be able to use the
information just covered about the decimal system to easily relate the same terms to the binary system.
Unit and Number
The base, or radix¾you should remember from our decimal section¾is the number of symbols used
in the number system. Since this is the base 2 system, only two symbols, 0 and 1, are used. The base is
indicated by a subscript, as shown in the following example:
12
When you are working with the decimal system, you normally don't use the subscript. Now that you
will be working with number systems other than the decimal system, it is important that you use the
subscript so that you are sure of the system being referred to. Consider the following two numbers:
11 11
With no subscript you would assume both values were the same. If you add subscripts to indicate
their base system, as shown below, then their values are quite different:
1110 112
The base ten number 1110 is eleven, but the base two number 112 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 you
MUST use the proper Subscript.
Positional Notation
As in the decimal number system, the principle of positional notation applies to the binary number
system. 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 the
positions and the powers of the base is shown below:
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