What does Ci-1 of a full adder mean? I haven’t been able to understand it after studying for a long time.

Give you the simplest example:

Take decimal calculation as an example: 146 287=? ?

If the units digits are added, it should be 6 7 0 = 13. The 1 in the summation result 13 is the carry to the high-order tens digit, which is Ci in your truth table; 3 That's Si.

The 0 in the addition formula 6 7 0 is Ci-1. Because it is the lowest bit, there is no carry signal if it is lower than it.

If the tens digits are added, it should be 4 8 plus the carry 1 generated by each digit, so the addition is: 4 8 1=13.

The 1 in the summation result 13 is the carry to the high-order hundreds, which is Ci in your truth table; 3 is Si.

The 1 in the addition formula 4 8 1 is Ci-1. Because it is the second-lowest bit, the single bit lower than it generates a carry signal 1 to it, so Ci-1 at this time is 1. .

In fact, the rules of binary addition and decimal addition are exactly the same, except that one is "when every two is added to one" and the other is "when every ten is added to one". A full adder is a circuit that implements the addition of a certain binary number. The addition of multiple binary numbers requires the cooperation of multiple full adders.

The English name of the full adder is full-adder. It is a combination circuit that uses a gate circuit to add two binary numbers and find the sum. It is called a one-bit full adder. A one-bit full adder can handle the low-bit carry and output the local addition carry. A multi-bit full adder can be obtained by cascading multiple one-bit full adders.

The expression for a one-bit full adder is as follows:

Si=Ai⊕Bi⊕Ci-1

The second expression can also be used with an XOR gate to replace the OR gate to sum the two input signals:

Three modeling methods of the hardware description language Verilog for a one-bit full adder: