Half Adder Sum Carry Boolean Pair Checker
Compute the Boolean sum and carry bits of a half adder.
Description
A half adder combines two single-bit inputs into a sum bit and carry bit.
A half adder combines two single-bit inputs into a sum bit and carry bit. The sum records odd parity and the carry records both inputs being one.1
The tool returns sum, carry. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Half Adder Sum Carry Boolean Pair Checker
Use this for the following task: Compute the Boolean sum and carry bits of a half adder. Prepare the specified logical encoding before running the check or transformation.
How to use Half Adder Sum Carry Boolean Pair 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 according to the field table, then run the tool.
- Read sum, carry. 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 |
Supply Boolean a and b. Evaluate their inequality for sum and conjunction for carry.
sum = a XOR b; carry = a AND b The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| sum | Sum | boolean |
| carry | Carry | boolean |
{
"input": {
"a": true,
"b": true
},
"output": {
"sum": false,
"carry": true
}
}Limitations and assumptions
This represents a single ideal combinational step. It does not accept a carry input or simulate timing, voltage or a multi-bit circuit.
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 Full Adder Majority Carry Expression Checker when you need its operation: Compute the Boolean sum and majority carry bits of a full adder with a carry input. 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
- Full Adder Majority Carry Expression Checker
Compute the Boolean sum and majority carry bits of a full adder with a carry input.
- XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) Checker
Evaluate XOR and its classical conjunction/disjunction expansion on two Boolean inputs.