Carry In

CARRY IN

There are 10 types of people in this world�
those who know binary, and those who don't.

Loo and LooLoo liked their two digit adder, but they wondered if they could extend it further so it would add a carry in digit. As in their previous project, they made a table of all the combinations. This new table, however, had 3 inputs:

the first digit
the second digit
the carry in digit.

This table showed all the possibilities of adding three digits together. They let C represent the carry in digit. With 3 inputs, they found 8 possible combinations. Notice the last column adds three 1's together. Notice also that they have ignored the carry out digit�for now. (Guess what the next assignment is?)


C       0   0   0   0   1   1   1   1
A       0   0   1   1   0   0   1   1
B       0   1   0   1   0   1   0   1
��������������������������������������
SUM     0   1   1   0   1   0   0   1

Note: Do not confuse the table above as the sum of two Looloolo numbers.
Think 8 different 1 digit sums, with each column a separate sum and the carry out ignored.
Turning their table sideways, and flipping to a mirror image, makes it look more familiar. (Yes, you have seen tables like this before somewhere!)

 
    C A B | SUM
    ___________

0)  0 0 0 |  0
1)  0 0 1 |  1
2)  0 1 0 |  1
3)  0 1 1 |  0
4)  1 0 0 |  1
5)  1 0 1 |  0
6)  1 1 0 |  0
7)  1 1 1 |  1
    ___________

Notice that rows 0 to 3 have no carry in digit. Rows 0 to 3 are the same as your previous assignment. Rows 4 to 7 show that the carry in digit reverses the output of rows 0 to 3. Can you diagram Loo's and LooLoo's carry in system?

ASSIGNMENT

For 2 points, write an expression for the CAB table using AND OR NOT symbols.
For 2 more points,
draw your expression in the Pipes applet using AND OR NOT blocks.
If you use 8 blocks or less, you earn 3 points extra.
Copy and save it as a gif file.
Then send it to me privately as an attachment in a message.

Last Modified 10/8/06 10:24 AM

Hide Tools

Site
Changes
Index
Search

User
Log In