1) Binary addition and subtraction follow similar rules to decimal with 0+0=0, 0+1=1, 1+0=1, 1+1=10, and 1+1+1=11. To subtract larger binary numbers, subtract column by column. 2) 1's complement changes each 0 to 1 and vice versa, and is used to subtract by adding the 1's complement of the subtrahend to the minuend. 2's complement is 1's complement plus 1. 3) 2's complement subtraction discards any end around carry, while 1's and 2's complement allow binary subtraction. 9's and 10's complement work similarly to convert decimals.

1. BINARY ADDITION
Binary additions ais accomplished in a manner similar to that in the decimal
number system.
RULES:
1. 0+0=0
2. 0+1=1
3. 1+0=1
4. 1+1=10
5. 1+1+1=11
EXAMPLE:
1011
1010 +
10101
BINARY SUBTRACTION:
Binary subtraction involves four basic rules which must be understood before
performing subtraction of larger binary members.
RULES:
1. 0-0=0
2. 1-0=1
3. 1-1=0
4. 10-1=1
COLUMN BY COLUMN SUBTRACTION:
To subtract large a binary numbers, we follow the same established system as
with the decimal numbers.
EXAMPLE:
Subtract 1 0 1 0 from 1 1 0 0
1100
1010 _
0010

2. 1’s COMPLEMENT:
The 1’s complement of a binary number is the number that results when we
change each 0 to a 1,and each 1 to a 0.
EXAMPLE:
(a) The 1’s complement of 1 0 0 1. is 0 1 1 0
1’s Complement Subtraction:
In 1’s complement subtraction the 1’s complement of the subtrahend is added to
the minuend.
Subtract 1 1 0 1 from 1 0 1 0
EXAMPLE:
11011
10010 +
101101
1
+01110
2’s COMPLEMENT :
The 2’s complement of a binary number is obtained by adding 1 to its 1’s
complement .
FORMULA:
2’s complement = 1’s complement +1
Ex:
Number 2’s complement
1110 0001+1=0010
0001 1110+1=1111
2’s COMPLEMENT SUBTRACTION:
In the 2’s complement subtraction as in the 1’s complement subtraction,
The 2’s complement of the subtrahend is added to the minuend, but the end-around
Carry if generated, is disregared.

3. EXAMPLE:
111
011 +
1010
{ discard in the carry 1}
9’s COMPLEMENT AND 10’s COMPLEMENT:
In the 9’s complement is found by subtracting each decimal digit from 9
9999
6291 _
3708
{ the 9’s complement of 6 2 9 1 }
The 10’s complement of a decimal integer is 1 greater then the 9’s complement
10’s complement = 9’s complement +1
EXAMPLE;
9999
6291 _
3 7 0 8 +1=3709