1-Column Addition - Three Digit Addition

Three bit addition consists of adding the two digits in the addends a, b, and the carry from the column to the right cin to produce sum and cout

The Boolean expressions for these two outputs are:

sum =
(~a · ~b · cin) + (~a · b· ~cin) + (a · ~b · ~cin) + (a· b · cin)

cout =
(~a· b · cin) + (a · ~b· cin) + (a · b · ~cin) + (a· b · cin)

Which can be seen in the Truth Table:

INPUTOUTPUT
a
b
cin
cout
sum
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1

 

PROBLEM:

Verify that the above equations can be derived from this table. The following may help you:

 
INPUT OUTPUT Term
a
b
cin
cout
 
0
0
0
0
 
0
1
0
0
 
1
0
0
0
 
1
1
0
1
 
0
0
1
0
 
0
1
1
1
(~a· b · cin)
1
0
1
1
 
1
1
1
1
 

 

INPUT OUTPUT Term
a
b
cin
sum
 
0
0
0
0
 
0
1
0
1
 
1
0
0
1
 
1
1
0
0
 
0
0
1
1
(~a · ~b · cin)
0
1
1
0
 
1
0
1
0
 
1
1
1
1
 

 

Fill in the remainder of the white rows yourself.

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Last Updated 2002/02/17
© L.Heath 2000, updated by J.A.N. Lee.