K Map Solver – Karnaugh Map Calculator

Build a Karnaugh map from minterms, maxterms or a truth table, then get a fully simplified Boolean expression with colored groupings. Supports 2–6 variables and don't-care conditions.

1. Define your Boolean function

Tip: click cells to toggle 0 → 1 → X (don't-care).

2. Edit the Karnaugh map

Gray code ordering is used on rows and columns. For 5–6 variables, two 4-variable maps are stacked as separate planes.

3. Simplify the Boolean expression

The solver finds prime implicants and selects a minimal cover using a Quine–McCluskey style algorithm adapted to K maps.

Results

Simplified Sum of Products (SOP) 


                

                

                  

                    Simplified Product of Sums (POS)
                  

                  

                

                

                  

                    Prime implicants & groups
                  

                  
    
                
    
              
    
            
    

            
            
    
              
    How this K map solver works
    
              
    
                This Karnaugh map calculator lets you simplify Boolean
                expressions for 2, 3, 4, 5 and 6 variables. You can start from
                minterms, maxterms or a full truth table, then interactively
                edit the K map and see the minimized SOP and POS forms.
              
    

              
    Supported input formats
    
              
      
                
    • 
                  Minterms (SOP): list the decimal indices
                  where the function is 1. Example for 4 variables:
                  1,3,7,11,15 or ranges like 0-3,8-11.
                
      • 
                
    • 
                  Maxterms (POS): list the indices where the
                  function is 0. The solver internally complements them.
                
      • 
                
    • 
                  Truth table: a comma- or space-separated list
                  of 0, 1 and
                  X (don't-care) values in ascending index order.
                
      • 
              
    
              
    
                After building the map, you can click any cell to toggle between
                0 → 1 → X. X cells are treated as don't-cares:
                they may be used to form larger groups but do not force the
                output to be 1.
              
    

              
    Gray code ordering
    
              
    
                K maps use Gray code ordering so that adjacent cells differ by
                only one variable. For example, with 4 variables:
              
    
              
    
                
    Row labels (AB): 00, 01, 11, 10
    
                
    Column labels (CD): 00, 01, 11, 10
    
              
    
              
    
                The solver automatically arranges rows and columns in Gray code
                and maps each minterm index to the correct cell.
              
    

              
    Grouping rules used by the solver
    
              
      
                
    • 
                  Groups must contain only 1s and optional don't-cares (X).
                
      • 
                
    • Group sizes are powers of two: 1, 2, 4, 8, 16, …
      • 
                
    • 
                  Groups can wrap around edges (top–bottom, left–right, and
                  between planes for 5–6 variables).
                
      • 
                
    • 
                  Each 1 must be covered by at least one group; essential prime
                  implicants are always included.
                
      • 
              
    
              
    
                Internally, the tool enumerates candidate groups, filters prime
                implicants, then selects a minimal cover using a heuristic
                similar to the Quine–McCluskey method but optimized for the K
                map geometry.
              
    

              
    From groups to Boolean terms
    
              
    
                Each group corresponds to a product term (for SOP) or a sum term
                (for POS). Variables that change within the group are
                eliminated; variables that stay constant appear in the term.
              
    
              
    
                
    Example (4 variables A, B, C, D):
    
                
      
                  
    • 
                    A group covering cells where A = 1 and
                    B = 0, while C and D vary, gives the term
                    A B'.
                  
      • 
                  
    • 
                    A group covering cells where C = 0 only gives
                    the term C'.
                  
      • 
                
    
              
    

              
    Example: 4-variable K map simplification
    
              
    
                Suppose you have minterms m(1,3,7,11,15) for
                variables A, B, C, D.
              
    
              
      
                
    1. 
                  Enter 1,3,7,11,15 as minterms and build the K
                  map.
                
      2. 
                
    2. 
                  The solver finds two groups: one group of 4 and one group of 2
                  cells.
                
      3. 
                
    3. 
                  It outputs something like:
                  
      
                    
      
                      SOP: \( F(A,B,C,D) = A' C D + B C D \)
                    
      
                  
      
                
      4. 
              
    

              
    When to use a K map vs. algebraic methods
    
              
      
                
    • 
                  K maps: best for up to 5–6 variables; they
                  give a visual, intuitive simplification.
                
      • 
                
    • 
                  Algebraic methods / Quine–McCluskey: scale
                  better to many variables but are harder to do by hand.
                
      • 
              
    
              
    
                This solver combines both: it uses the K map layout for
                visualization and a systematic algorithm to guarantee a minimal
                or near-minimal expression.
              
    

              
    Common mistakes K maps help you avoid
    
              
      
                
    • Forgetting wrap-around adjacency on the edges.
      • 
                
    • Using groups that are not powers of two.
      • 
                
    • Missing essential prime implicants.
      • 
                
    • Not using don't-care cells to form larger groups.
      • 
              
    
              
    
                By highlighting each group in a different color and listing the
                corresponding term, this tool makes it easy to verify your
                manual solution or learn the technique step by step.
              
    

              
    FAQ
    
              
    Can this K map solver handle multiple output functions?
    
              
    
                This version focuses on a single output function at a time. To
                simplify multiple outputs, solve each function separately using
                the same truth table inputs.
              
    

              
    How are 5- and 6-variable K maps displayed?
    
              
    
                For 5 variables, the map is split into two 4-variable planes
                (e.g., A=0 and A=1). For 6 variables, two planes are used for
                the two most significant variables. The solver still returns a
                single simplified expression in terms of all variables.
              
    

              
    What notation is used for complements?
    
              
    
                By default, the solver uses a prime notation such as
                A' for NOT A. You can copy the expression directly
                into most digital logic textbooks or convert it to overbar
                notation if needed.