Logic guides

Guides to the questions users ask most about logic. Truth tables marked “Computed by the Tangibool engine” come straight from the engine, and every tool result a guide links to is re-checked by the engine whenever the site is built.

• BCD to seven-segment decoder
  A BCD to seven-segment decoder turns a 4-bit decimal digit, 0000 to 1001, into the seven signals a to g that light a display's segments.10 min read
• Binary to Gray code
  Gray code is a binary code in which consecutive numbers differ in exactly one bit.10 min read
• What is Boolean logic?
  Boolean logic is the logic of true and false. Every statement has one of two values, and AND, OR and NOT combine statements into larger ones.13 min read
• Boolean operators
  Boolean operators are the words AND, OR and NOT used to combine search terms or conditions.9 min read
• Conditional statements
  A conditional statement says “if p, then q”, written p → q. The part after “if” is the hypothesis and the part after “then” is the conclusion.12 min read
• What is discrete math?
  Discrete math is the mathematics of things that come in separate, countable pieces: whole numbers, true and false, sets, networks and step-by-step processes.18 min read
• Encoders and decoders
  A decoder turns an n-bit code into 2ⁿ output lines, exactly one of them active: each output is one minterm of the inputs.9 min read
• Flip-flop truth tables
  A flip-flop stores one bit and changes it only on a clock edge.14 min read
• Half adder and full adder
  A half adder adds two bits and outputs a sum and a carry: sum = A XOR B, carry = A AND B.15 min read
• Half subtractor and full subtractor
  A half subtractor computes A − B for two bits: the difference is A XOR B and the borrow is A′·B, which is 1 only for 0 − 1.10 min read
• How to make a truth table
  To make a truth table, list every combination of true and false for the variables (2ⁿ rows for n variables), add one column for each part of the expression from the inside out, and fill each column…10 min read
• What is a logic gate?
  A logic gate is a small circuit, or its symbol on a diagram, that takes one or more inputs, each 0 or 1, and gives one output by a fixed rule: its truth table.18 min read
• Multiplexer truth tables
  A multiplexer, or mux, is a data selector: its select lines choose which of its data inputs reaches its one output.12 min read
• Necessary and sufficient conditions
  A sufficient condition guarantees the outcome; a necessary condition is required for it.10 min read
• Rules of inference
  Rules of inference are the valid steps of a logical proof: patterns such as modus ponens, “if p then q; p; so q”, that always lead from true premises to a true conclusion.12 min read
• SQL IS NULL and IS NOT NULL
  In SQL, NULL means “unknown”, so col = NULL is never true: test for a missing value with col IS NULL and for a present one with col IS NOT NULL.9 min read
• SR latch and D latch
  A latch is the simplest memory circuit: two gates that feed each other hold one bit.9 min read
• Valid vs sound arguments
  An argument is valid when its conclusion must be true whenever all its premises are true; validity is about form.10 min read
• Converse, inverse and contrapositive
  The contrapositive of “if p, then q” is “if not q, then not p”, and it is always true or false together with the original statement.18 min read