Transcript 1`s complement method

1’s and 2’s Complements
Introduction
• Subtraction of a number from another can be
accomplished by adding the complement of the
subtrahend to the minuend.
1’s Complement Subtraction
• Subtraction of binary numbers using the 1’s complement
method allows subtraction only by addition.
• The 1’s complement of a binary number can be obtained by
changing all 1s to 0s and all 0s and 1s.
1’s complement method
• To subtract a smaller number from a larger number, the
1’s complement method is as follows
1. Determine
2.
3.
Add this the
Remove
tothe
the
carry
1’s
larger
complement
andnumber
add it to of
thethe
result.
smaller
Thisnumber.
carry is
called end-around-carry
Example of 1’s complement
Subtract (1010)2 from (1111) 2
1’s complement method
Direct Subtraction
1 1 1 1
1 0 1 0
0 1 0 1
1 1 1 1
1’s complement
Carry
Add Carry
0 1 0 1
1 0 1 0 0
1
0 10 1
Subtraction Steps
• Subtraction of a large number a smaller one by the 1’s
complement method involves the following steps
1. The
2.
3.
Determine
Add
answer
this to the
the
is the
1’s
smaller
1’s
complement
complement
number of of
a large
the result
number
and is
opposite in sign. There is no carry.
2’s Complement Subtraction
• The 2’s complement of a binary number can be
obtained by adding 1 to its 1’s complement.
Steps
• Subtraction of a smaller number from a larger one by
the 2’s complement method involves the following
steps
1.
2.
3.
Determine
the (2’s
complement
the smaller
number
Add this
Omit
theto
carry
larger
there
number
is always of
a carry
in this case
)
Example of 2’s complement
Subtract (1010)2 from (1111) 2
Direct Subtraction
2’s complement method
1 1 1 1
1 1 1 1
1 0 1 0
2’s complement
0 1 1 0
0 1 0 1
Carry
1 0 1 0 1
Subtraction Steps
• The carry is discarded. Thus answer is (0101)2
• The 2’s complement method for subtraction of a
large number from a smaller one is as follows.
1. To
2.
3.
Determine
Add
There
the
isanno
2’sanswer
the
carry
complement
2’s. in
The
complement
result
to
the
is in
smaller
of
2’s
thecomplement
larger
number
form
4.
get
true
form,
take
the
2’s number
is
negative and change the sign.
complement
Comparison between 1’s and 2’s
complements
1’s Complement
2’s Complement
It can be easily obtained using
an Inverter
It has to be arrived at by first
obtaining the 1’s complement
and then adding one (1) to it
It requires two operations
Only one arithmetic operation is
required
It is often used in logical
manipulations for inversion
operation
It is used only for arithmetic
applications