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When you input text, the character encoding maps characters we choose to specific bytes in computer memory.
To output the same, it reads the bytes back into characters. A character encoding provides a key to unlock this binary
code. It is a set of mappings between the bytes in the computer and the characters in the character set.
Definition
Character encoding is a process of assigning numeric code to character set of different human languages across the
world, allowing them to be stored, computed, converted and transmitted using digital computers.
2.1 BINARY ENCODING FOR INTEGERS
Integers are the numbers without decimal point. They can be positive, negative or zero. Digital devices work on binary
integers which can be unsigned or signed. Unsigned binary numbers can represent positive values only and signed
binary numbers can represent both positive and negative values. Writing prefix + sign is not mandatory for positive
numbers. However, giving the ‘-’ sign before a negative number is compulsory.
In digital computers, a decimal number when converted internally to binary cannot have a + or - sign as digital circuits
have no such provision. So, the need for separate representation arises.
Thus, binary integers both unsigned and signed are represented in three ways which are as follows:
• Signed magnitude notation
• One’s complement notation
• Two’s complement notation
2.1.1 Signed Magnitude Notation
The signed magnitude notation is the representation of a signed binary number. If the sign bit is “0”, the number is
positive. If the sign bit is “1”, then the number is negative.
Let us illustrate this with an example. Consider an integer number 67. Its binary equivalent is 1000011. Considering
8-bit byte, +67 and -67 will be represented as follows:
+67 0 1 0 0 0 0 1 1
-67 1 1 0 0 0 0 1 1
Sign bit Value bits
So we see that in this representation with an n-bit field, the range of numbers that can be represented is:
-2 n-1 - 1 to 2 n-1 - 1
For example: if we have 8 bits to represent a signed binary number (i.e., 1-bit for the Sign bit and 7-bits for the
Magnitude bits), then the actual range of numbers we can represent in signed magnitude notation would be:
-2 (8-1) - 1 to +2 (8-1) - 1
-127 to +127
Definition
Signed magnitude notation is a way of representing binary numbers of ‘n’ bits by reserving 1 bit in leftmost MSB
for sign and remaining n-1 bits for the magnitude. The sign bit is assigned 0 for positive binary numbers and 1 for
negative numbers.
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