ADDING 2 2-bit numbers
The two 2 bit numbers are A1A0 and B1B0. A0 & B0 are the least significant bits.
We will set CIN to zero to test this circuit.
There are four inputs and the easiest way to check all possible combinations is to list them in order A0 A1 B0 B1 .
The write out the binary numbers 0000 to 1111 in the columns.
Using the Half Adder truth table then we can work out the following truth table.
|
A |
B |
Carry |
COUT |
Sum1 |
Sum0 |
A1A0+ B1B0 |
||
|
A0 |
A1 |
B0 |
B1 |
|||||
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
00+ 00 |
|
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
00+ 10 |
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
00+ 01 |
|
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
00+ 11 |
|
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
10+ 00 |
|
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
10+ 10 |
|
0 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
10+ 01 |
|
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
10+ 11 |
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
01+ 00 |
|
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
01+ 10 |
|
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
01+ 01 |
|
1 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
01+ 11 |
|
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
11+ 00 |
|
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
11+ 10 |
|
1 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
11+ 01 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
11+ 11 |
The output from this circuit is COUT Sum1 Sum0.
Check this with the additions
A1A0+
B1B0