1-column addition

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 c_in to produce sum and c_out

The Boolean expressions for these two outputs are:

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

c_out =
(~a· b · c_in) + (a · ~b· c_in) + (a · b · ~c_in) + (a· b · c_in)

Which can be seen in the Truth Table:

INPUT			OUTPUT
a	b	*c_in*	*c_out*	*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 c_in c_out

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 · c_in)

1 0 1 1

1 1 1 1

INPUT	OUTPUT	Term
a	b	*c_in*	*c_out*
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 · c_in)*
1	0	1	1
1	1	1	1

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

Fill in the remainder of the white rows yourself.