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Binary Addition &
Subtraction
Addition Rules
• 0 + 0 = 00 ( 0 with a 0 carry )
• 0 + 1 = 01 ( 1 with a 0 carry )
• 1 + 0 = 01 ( 1 with a 0 carry )
• 1 + 1 = 10 ( 0 with a 1 carry )
Addition Rules
0
+0
0 0
1
+0
0 1
0
+1
0 1
1
+1
1 0
4
Addition Rules w/Carries
• 0+0+0 = 00 (0 WITH 0 CARRY)
• 0+0+1 = 01 (1 WITH 0 CARRY)
• 0+1+1 = 10 (0 WITH 1 CARRY)
• 1+1+1 = 11 (1 WITH 1 CARRY)
Adding Binary Numbers
0 1 1 1 0 0 0
28
+ 43
71

00011100
 + 00101011
01000111
6
1’S Complement
01010011

Invert All Bits
10101100
7
2’S Complement
01010011

Invert All Bits
Add One
10101100
+1
10101101
8
Add/Sub : 4 Combinations
Positive / Positive
Positive Answer
9
+ 5
14
Positive / Negative
Positive Answer
9
+ (-5)
4
Negative / Positive
Negative Answer
(-9)
+ 5
-4
Negative / Negative
Negative Answer
(-9)
+ (-5)
- 14
9
Positive / Positive Combination
Positive / Positive
Positive Answer
9
+ 5
14



00001001
+ 00000101
00001110
Both Positive Numbers
Use Straight Binary Addition
10
Positive / Negative Combination
Positive / Negative
Positive Answer
9
+ (-5)
4
1-Positive / 1-Negative
Take 2’s Complement
Of Negative Number (-5)


00001001
+ 11111011
1]00000100
8th Bit = 0 : Answer is Positive
Disregard 9th Bit
00000101

11111010
+1
11111011
2’s
Complement
Process
11
Negative / Positive Combination
Positive / Negative
Negative Answer
(-9)
+ 5
- 4
1-Positive / 1-Negative
Take 2’s Complement
Of Negative Number (-9)
11111100
2’s
Complement
Process

00000011
+1
00000100

11110111
+ 00000101
11111100
8th Bit = 1 : Answer is Negative
Take 2’s Complement to Check Answer
00001001

11110110
+1
11110111
2’s
Complement
Process
12
Negative / Negative Combination
Negative / Negative
Negative Answer
(-9)
+ (-5)
- 14
2-Negative
Take 2’s Complement Of
Both Negative Numbers


11110111
+ 11111011
2’s Complement
Numbers, See
Conversion
Process
In Previous Slides
1]11110010
8th Bit = 1 : Answer is Negative
Disregard 9th Bit
Take 2’s Complement to Check Answer
11110010
2’s
Complement
Process

00001101
+1
00001110
13
2’S Complement Quick Method
Example:
11101100
1) Start at the LSB and write down all zeros moving
to the left.
2) Write down the first “1” you come to.
3) Invert the rest of the bits moving to the left.
0 001 0 1 0 0
14