Non-Negative Binary System
In this System each bit position represents a power of 2.
The right most bit position represent 20 which equals 1.
The next position to the left represents 21= 2 and so on.
An Integer is represented as a sum of powers of 2. A string
of all 0s represents the number 0. If a 1 appears in a
particular bit position, the power of 2 represented by that
bit position is included in the Sum. But if a 0 appears, the
power of 2 is not included in the Sum. For example 10011,
the sum is 19
Ones Complement Notation
Negative binary number is represented by ones Complement Notation.
In this notation we represent a negative number by changing each bit
in its absolute value to the opposite bit setting. For example,
since 001001100 represent 38, 11011001 is used to represent -38. The
left most number is reserved for the sign of the number. A bit String
Starting with a 0 represents a positive number, where a bit string
starting with a 1 represents a negative number.
Twos Complement Notation
In Twos Complement Notation is also used to represent a negative number.
In this notation 1 is added to the Ones Complement Notation of a negative
number. For example, since 11011001 represents -38 in Ones Complement
Notation 11011010 used represent -38 in Twos Complement Notation.
Binary Coded Decimal
In this System a string of bits may be used to represent integers in
the Decimal Number System . Four bits can be used to represent a Decimal
digit between 0 and 9 in the binary notation. A string of bits of arbitrary
length may be divided into consecutive sets of four bits. With each set
representing a decimal digit. The string then represents the number that is
formed by those decimal digits in conventional decimal notation.
For example, in this system the bit string 00110101 is separated into
two strings of four bits each: 0011 and 0101. The first of these represents
the decimal digit 3 and the second represents the decimal 5, so that
the entire string represents the integer 35.
In the binary coded decimal system we use 4 bits, so this four bits
represent sixteen possible states. But only 10 of those sixteen
possibilities are used. That means, whose binary values are 10 or
larger, are invalid in Binary Coded Decimal System.
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