Binary Adders
Curriculum[edit]
Coder Merlin™ Computer Science Curriculum Data  
Unit: Boolean algebra Experience Name: Binary Adders (W1017) Knowledge and skills:
Topic areas: Boolean algebra Classroom time (average): 30 minutes Study time (average): 60 minutes Successful completion requires knowledge: understand the construction and use of binary adders Successful completion requires skills: demonstrate proficiency in constructing and using binary adders 
Introduction[edit]
One of the most fundamental operations performed by computers, aside from the logical operations that we've already discussed, is the arithmetic operation of addition.
HalfAdder[edit]
Let's consider what's required to add two, singlebit binary integers. We'll need one bit to represent the sum of the integers, and another to handle the carry. Representing this in the form of a truth table yields:
Inputs  Outputs  

0  0  0  0 
0  1  0  1 
1  0  0  1 
1  1  1  0 
This is formally termed a halfadder, a logic circuit capable of adding two bits.
Observe, Ponder, and Journal Section 1  

FullAdder[edit]
In order to add two singlebit binary integers PLUS a carry, we need an adder capable of adding three singlebit binary numbers. Again, we'll need one bit to represent the sum of the integers, and another to handle the carry. Representing this in the form of a truth table yields:
Inputs  Outputs  

0  0  0  0  0 
0  0  1  0  1 
0  1  0  0  1 
0  1  1  1  0 
1  0  0  0  1 
1  0  1  1  0 
1  1  0  1  0 
1  1  1  1  1 
This is formally termed a fulladder, a logic circuit capable of adding three bits.
Observe, Ponder, and Journal Section 2  

Ripple Carry Adder[edit]
We've learned that a halfadder can add two bits and fulladder can add three bits. How can we add a multibit number such as a 16bit word? By cascading four adders such that the carry output of the prior adder feeds the carry input of the subsequent adder we can add two fourbit numbers. This concept can be easily extended to an arbitrary number of bits.
Observe, Ponder, and Journal Section 3  

Key Concepts[edit]
Key Concepts  

Exercises[edit]
Exercises  

References[edit]
 Adder (Wikipedia)
 Schocken, Simon and Nisan, Noam. The Elements of Computing Systems. MIT Press, 2005.
Experience Metadata
Experience ID  W1017 

Unit  Boolean algebra 
Knowledge and skills  §10.331 
Topic areas  Boolean algebra 
Classroom time  30 minutes 
Study time  1 hour60 minutes <br /> 
Acquired knowledge  understand the construction and use of binary adders 
Acquired skill  demonstrate proficiency in constructing and using binary adders 
Additional categories 