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Signed Binary Numbers
In ordinary arithmetic a negative number is indicated by
minus sign and positive number by plus sign. This is not
possible in computers, because of hardware limitation
computers must represent everything with binary digits.
There are two methods to do this:
The signed magnitude convention uses the left-most bit to represent the
sign (0 for positive and 1 for negative).
The signed complement system negates a number by taking its
complement.
It could be either, 1 ’s complement representation
or 2 ’s complement representation.
Signed Magnitude Convention The signed magnitude convention uses the left-most bit to
represent the sign (0 for positive and 1 for negative).
The user determines whether the number is signed or unsigned
If the binary number is signed then the leftmost bit represents the sign and
the rest of the bits represents the number
If the binary number is unsigned then the leftmost bit is the most
significant bit of the number
For example:
01001 can be considered as 9 (unsigned binary) or a +9 because the
left most bit is zero.
On the other hand, the string of bits 11001 represents binary equivalent
of 25 when considered as an unsigned number or as – 9 when considered as signed number 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 sign bit Negative Positive
Number Representations
The following is the representation for +11:
The following are different methods for representing -11:
Signed magnitude: 10001011
Signed-1’s-complement: 11110100
Signed-2’s-complement: 11110101
Signed Binary Numbers
Arithmetic Addition (Signed 2’s Complement system) This system doesn’t require the comparison of the signs
and the magnitudes (as in signed-magnitude system), but
only addition.
The addition of two signed binary numbers with negative
numbers represented in signed-2’s complement form is
obtained from addition of the two numbers, including their
sign bits.
A carry out of the sign-bit position is discarded. If the sum is negative, it will be in 2’s complement form.
Arithmetic Subtraction
Subtraction can be performed by simply converting the
equation into an addition formula.
Take the 2’s complement of the subtrahend (including the sign bit) and
add it to the minuend (including the sign bit)
A carry out of the sign bit position is discarded
Note: Subtraction operation can be changed to an addition operation if the
sign of the subtrahend is changed. This is easily done by taking it’s 2’s complement
Example
Consider the subtraction (–6) – (–13) = +
In binary with eight bits the same is written as (11111010 –
This subtraction is changed to addition by taking 2 ’s
complement of the subtrahend (– 13) to give (+ 13)
In binary this is 11111010 + 00001101 = 100000111
Removing the end carry, we obtain the correct answer:
The End
