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An integer number 67 is represented as 8-bit binary number 01000011. -67 will be represented in 1’s complement
notation as 10111100 just by flipping 0’s and 1’s.
+67 0 1 0 0 0 0 1 1
-67 1 0 1 1 1 1 0 0
One’s complement notation
n
For an ‘n’ bit number, one’s complement notation can represent 2 - 1 numbers in the range from -2 (n-1) - 1 and
+2 (n-1) - 1.
The range for different bit fields is represented in the following tabular form:
Bit notation Range for 1's complement numbers
4 -7 to +7
8 -127 to +127
16 -32767 to +32767
Definition
One’s complement representation of a binary negative number is obtained by changing 0 bit to 1 and 1 bit to
0 starting from the rightmost LSB to the leftmost MSB. The representation of a binary positive number remains
unchanged.
Advantage of One’s complement method:
• Binary addition and subtraction using signed and unsigned numbers can be done conveniently with this method.
Disadvantages of One’s complement method:
• It is an unconventional way of representing signed integers.
• Ambiguous representation of 0. Considering 8-bit byte, +0 is represented as 00000000 whereas -0 as 11111111. This
becomes inconvenient for digital devices to interpret.
Note: The method has been described in detail in Chapter 1 of this book.
Example 1: Find the 1’s complement representation of -17 expressed in 8-bit notation.
Binary equivalent of +17 is: 00010001
One’s complement of -17 is: 11101110
Example 2: Find the 1’s complement representation of -0 expressed in 8-bit notation.
Binary equivalent of +0 : 0000 0000
One’s complement of -0 : 1111 1111
2.1.3 Two’s Complement Notation
The binary equivalent of integer number 67 is 01000011. Its 1’s complement obtained by toggling 0 and 1 is 10111100.
2’s complement will be 10111100 + 1 = 10111101.
+67 0 1 0 0 0 0 1 1
-67 1 0 1 1 1 1 0 1
Two’s complement notation
49
Encoding 49

