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Unformatted text preview: number system. It is important only to keep track of the base of the number system in
which we are working.
The following two characteristics are suggested by the value of the base in all positional
The value of the base determines the total number of different symbols or digits
available in the number system. The first of these choices is always zero.
2. The maximum value of a single digit is always equal to one less than the value of the
Some of the positional number systems commonly used in computer design and by
computer professionals are discussed below.
Binary Number System
The binary number system is exactly like the decimal number system except that the base
is 2 instead of 10. We have only two symbols or digits (0 and 1) that can be used in this
number system. Note that the largest single digit is 1 (one less than the base). Again, each
position in a binary number represents a power of the base (2). As such, in this system,
the rightmost position is the units (2°) position, the second position from the right is the
2's (21) position and proceeding in this way we have 4's (2 2) position, 8's (23) position,
16's (24) position, and so on. Thus, the decimal equivalent of the binary number 10101
(written as IOIOI2) is:
(1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 2°), or
16 + 0 + 4 + 0+1, or
In order to be specific about which system we are referring to, it is common practice to
indicate the base as a subscript. Thus we write:
101012 = 2110
"Binary digit" is often referred to by the common abbreviation bit. Thus, a "bit" in
computer terminology means either a 0 or a 1. A binary number consisting of 'n' bits is
called an n-bit number. Figure 3.1 lists all the 3-bit numbers along with their decimal equivalent. Remember that we have only two digits, 0 and 1, in the binary system, and
hence the binary equivalent of the decimal number 2 has to be stated as 10 (read as one,
zero). Another important point to note is that with 3 bits (positions), only 8 (2 3) different
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This document was uploaded on 04/07/2014.
- Spring '14