1. 2's Complement Arithmetic
Digital Electronics 
Lesson 2.4 – Specific Comb Circuit & Misc Topics
2’s Complement Arithmetic
Digital Electronics
© 2014 Project Lead The Way, Inc.
Project Lead The Way, Inc.
Copyright 2009

2. 2’s Complement Arithmetic
Digital Electronics 
Lesson 2.4 – Specific Comb Circuit & Misc Topics
This presentation will demonstrate
The 2’s Complement Process.
How the 2’s complement process can be used to add (and subtract) binary numbers.
That subtracting one number from another is the same as making one number negative and adding.
How to create negative numbers in the binary number system.
Introductory Slide / Overview of Presentation
Project Lead The Way, Inc.
Copyright 2009

3. Binary Addition Single Bit Addition: Multiple Bit Addition: Carry Cout
XOR, XNOR, & Adders
Digital Electronics
Lesson 2.4 – Specific Comb Circuit & Misc Topics
Single Bit Addition:
Carry
Multiple Bit Addition:
Cin
Cout A B
Sum
This slide shows the four possible combinations of adding together two single bit binary numbers and how these single bits can be cascaded into the addition of two 4-bit binary numbers. The 4-bit is just an example; we could have used 8-bits, 12-bits, etc.
Project Lead The Way, Inc.
Copyright 2009

4. 2’s Complement Examples
2's Complement Arithmetic
Digital Electronics 
Lesson 2.4 – Specific Comb Circuit & Misc Topics
Example #1
5 =
Complement Digits

Add 1 +1
-5 =
Example #2
Examples of the 2’s Complement Process.
-13 =
Complement Digits

Add 1 +1
13 =
Project Lead The Way, Inc.
Copyright 2009

5. 2's Complement Arithmetic
POS + POS → POS Answer
Digital Electronics 
Lesson 2.4 – Specific Comb Circuit & Misc Topics
If no 2’s complement is needed, use regular binary addition. 9
+ 5 14  +  
Addition of two Positive numbers.
Project Lead The Way, Inc.
Copyright 2009

6. 2's Complement Arithmetic
POS + NEG → POS Answer
Digital Electronics 
Lesson 2.4 – Specific Comb Circuit & Misc Topics
Take the 2’s complement of the negative number and use regular binary addition. 9
+ (-5) 4  +  1]
8th Bit = 0: Answer is Positive
Disregard 9th Bit
This example shows the addition of one positive and one negative numbers. Note that this is done in the same way as subtracting a positive number from a positive number. In this case, the answer is positive.
 +1
2’s
Complement
Process
Project Lead The Way, Inc.
Copyright 2009

7. 2's Complement Arithmetic
POS + NEG → NEG Answer
2's Complement Arithmetic
Digital Electronics 
Lesson 2.4 – Specific Comb Circuit & Misc Topics
Take the 2’s complement of the negative number and use regular binary addition.
(-9)
+ 5 -4  + 
8th Bit = 1: Answer is Negative
This slide demonstrates the addition of one positive and one negative number. Again, this is is the same a subtracting a positive number from a positive number. In this case the answer happens to be negative.
 +1
To Check:
Perform 2’s
Complement
On Answer
 +1
2’s
Complement
Process
Project Lead The Way, Inc.
Copyright 2009

8. 2's Complement Arithmetic
NEG + NEG → NEG Answer
2's Complement Arithmetic
Digital Electronics 
Lesson 2.4 – Specific Comb Circuit & Misc Topics
Take the 2’s complement of both negative numbers and use regular binary addition.
(-9)
+ (-5)
-14 
2’s Complement
Numbers, See
Conversion Process
In Previous Slides  +  1]
8th Bit = 1: Answer is Negative
Disregard 9th Bit
This slide demonstrates the addition of two negative numbers.
 +1
To Check:
Perform 2’s
Complement
On Answer
Project Lead The Way, Inc.
Copyright 2009