Full Adder Majority Carry Expression Checker
Compute the Boolean sum and majority carry bits of a full adder with a carry input.
Description
A full adder adds two bits and a carry-in.
A full adder adds two bits and a carry-in. The outgoing carry is true when a majority of the three inputs are true.1
The tool returns sum, carryOut. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Full Adder Majority Carry Expression Checker
Use this for the following task: Compute the Boolean sum and majority carry bits of a full adder with a carry input. Prepare the specified logical encoding before running the check or transformation.
How to use Full Adder Majority Carry Expression Checker and understand its results
- Prepare the requested Boolean values, complete truth-table rows, or identifier atoms. An atom is a name such as p or premise_1, not a natural-language sentence.
- Enter a, b, carryIn according to the field table, then run the tool.
- Read sum, carryOut. Use the matching rule, assignment order or nonempty-class assumptions below to interpret the result.
- For a false check, inspect the supplied encoding and matching rule. A well-formed false result is different from an input error.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| a | A | boolean | Required |
| b | B | boolean | Required |
| carryIn | Carry In | boolean | Required |
Supply three Booleans. Convert them to zero or one, sum them and return parity and the carry threshold flag.
total=a+b+carryIn; sum=total mod 2; carryOut=total≥2 The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| sum | Sum | boolean |
| carryOut | Carry Out | boolean |
{
"input": {
"a": true,
"b": true,
"carryIn": true
},
"output": {
"sum": true,
"carryOut": true
}
}Limitations and assumptions
The result is one ideal bit position. Wiring, propagation delay and multi-bit cascading are outside this calculation.
The supplied encodings must represent the intended propositions or classes. No natural-language parsing or assessment of empirical premise truth is performed. Malformed input gives a tool error rather than a logical false result.
Alternative or Complementary methods
Choose Half Adder Sum Carry Boolean Pair Checker when you need its operation: Compute the Boolean sum and carry bits of a half adder. Choose XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) Checker for the complementary operation: Evaluate XOR and its classical conjunction/disjunction expansion on two Boolean inputs.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- Half Adder Sum Carry Boolean Pair Checker
Compute the Boolean sum and carry bits of a half adder.
- XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) Checker
Evaluate XOR and its classical conjunction/disjunction expansion on two Boolean inputs.