Short answer
What you need to know
Choose Truth Tables for Boolean expressions, editable outputs and Karnaugh maps; Number Converter for decimal-to-binary, hex and ASCII; or Binary Calculator for fixed-width arithmetic and bitwise operations. Predict a small example first, run it, then explain why each result follows.
Follow the example one row at a time
| A | B | A' | Y = A' + B |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 |
1. Start with Y = A' + B
Open Truth Tables, select Load example, then Generate truth table. Here A' means NOT A and + means OR. Inputs A and B are listed alphabetically; rows are 00, 01, 10 and 11. The outputs are 1, 1, 0 and 1.
For row 10, A is 1 so A' is 0; B is also 0; therefore 0 OR 0 gives 0. For row 00, A' is 1, so the output is 1. Choose Explain on either row to compare your reasoning with the calculation steps. Show intermediate results to inspect individual operations.
2. Read the notation before calculating
Use single-letter inputs A–Z. NOT may be written A', !A or ~A. AND accepts A*B, AB or A&B. OR accepts A+B or A|B. XOR uses A^B and is true when exactly one of its two inputs is true. Constants 0 and 1 are allowed.
Precedence is NOT, AND, XOR, then OR. Thus A+B*C means A OR (B AND C), not (A OR B) AND C. Add parentheses when they make the intended grouping easier to read. Y = is an optional output label; Y cannot also be an input in that expression. Names such as ENABLE are interpreted as individual letters, not one named signal.
The generator supports eight distinct inputs, 256 rows, 2,000 characters and bounded nesting. Malformed expressions produce an error instead of a partial answer. Changing the source hides old results so they cannot be mistaken for the new expression's output.
3. Build an equation from desired outputs
Generate a starting table containing your desired inputs, such as A+B, then choose Edit output table. This creates a separate table for your design. To build XOR, set its four outputs to 0, 1, 1, 0, then select Generate verified equations.
The original table, its explanations and its CSV still describe the original expression. The edited table has its own CSV. Reset restores the original outputs; editing an output hides prior equations until you generate them again. Changing the source expression discards the edited table. Switching tools preserves the current workspace state.
Editing and exact simplification support at most four inputs (16 rows). Every edited row must be 0 or 1. Don't-cares, multiple outputs and gate diagrams are not supported in this release.
4. Canonical does not mean minimized
Canonical sum of products (SOP) makes one AND term for each row whose output is 1. Each term includes every input: complement inputs that are 0 and leave inputs that are 1 uncomplemented. Join those terms with OR. For XOR, rows 01 and 10 produce A'*B + A*B'.
A minimized SOP can omit inputs that do not affect a group of 1 rows. For outputs 1,1,0,1, the canonical expression is A'*B' + A'*B + A*B; the exact minimum SOP is A' + B. Both equations must reproduce all four outputs.
This tool minimizes the number of product terms first, then the total number of literal occurrences. Equal-cost solutions use the ASCII-lexicographically first expression after sorting terms. Other equally minimal answers can exist. This is an exact minimum within two-level SOP, not a claim of the shortest expression using XOR, factoring or every possible notation. Both equations are checked with the evaluator on every input assignment before display.
5. Read a Karnaugh map
A verified two-to-four-input edited table also shows a Karnaugh map. Two-bit axes run 00, 01, 11, 10: this Gray-code order changes one bit at a time, including the last-to-first edge. Do not use ordinary binary order 00,01,10,11 when copying the map.
Each group corresponds to one term of the exact minimum SOP. Groups contain 1, 2, 4, 8 or 16 output-1 cells in rectangles, possibly wrapping across opposite edges. Diagonals are not adjacent. Groups may overlap, and every 1 must be covered without including a 0. Select a group to highlight its cells and read which inputs stay fixed and which disappear.
Try B'*D'+0*A+0*C. The zero terms keep all four inputs in the starting table. Generate it, open the output editor, then generate equations. With AB on rows and CD on columns, the four corners are 1. Their group wraps both top-to-bottom and left-to-right. B and D stay 0 while A and C vary, so the term is B'*D'.
All-zero outputs need no groups and give expression 0. All-one outputs give one full-map group and expression 1. Constants and single-input tables have valid equations but no Karnaugh map here.
6. Check your work and keep useful evidence
Compare the canonical and minimized expressions against a few rows by hand, including at least one 0 row. Use intermediate values and row explanations for the original expression, and grouping explanations for edited outputs. Export the appropriate table as CSV when you need to keep it. Refreshing or leaving the page discards the workspace.
All expressions, operands, tables and results are processed in the browser. Successful generations, conversions and calculations send a content-free completion signal to the site's aggregate usage counter. No expression, number or output is sent in that signal. Counts represent activities, not unique students; group selection, edits and exports are not counted.
Try these before revealing the answers
For A=1, B=0, C=0, compare A+B*C with (A+B)*C.
Show worked answer
A+B*C is 1 OR (0 AND 0) = 1. (A+B)*C is (1 OR 0) AND 0 = 0. Parentheses change the function.
Which two-input outputs produce A*B?
Show worked answer
0,0,0,1 for rows 00,01,10,11. Only the all-one row makes AND true.
Why do the four corners in the worked map reduce to B'*D'?
Show worked answer
The corners have B=0 and D=0 in common; A and C take both values and can be removed. Opposite edges are adjacent in Gray-code order.
Your answer differs from the displayed minimum. Must it be wrong?
Show worked answer
No. Evaluate every row to check equivalence, then compare term and literal counts under the stated SOP objective. Equivalent expressions can have equal cost or use a different notation.
Important limitation
Know what the tool verifies
Use the explanations to support your own reasoning. The evaluator checks the specified Boolean function, not your circuit wiring, timing, hazards or assignment requirements. A minimum SOP is not a timing or hardware-area optimization.
Further reading
Authoritative references
These primary sources support the concepts and reference information in this guide. Their inclusion does not imply endorsement of Hidden Word Scanner.