KALK and WKALK: An introduction to Ancient Klingon Mathematics

KALK and WKALK provide a practical interface to the interesting world of ancient Klingon mathematics. Using a stack based base interface, the user can enter numbers, and execute the four basic arithmetic operations.

Ancient Klingon mathematics used a system based on three, with no zero.Compare counting in base ten to Klingon:

Counting:
 Base 10 1 2 3 4 5 6 7 8 9 10 Klingon 1 2 3 11 12 13 21 22 23 31

Simple Math operations

 + 1 2 3 1 2 3 11 2 3 11 12 3 11 12 13

Multiplication:
 x 1 2 3 1 1 2 3 2 2 11 13 3 3 13 23

Perform Klingon Math Online!

Enter Klingon numbers, and operations below to execute the Kalk program online

• . : print and pop stack

• + : add two top entries

• - : subtract two top entries (second - top)

• x : multiply two top entries

• / : divide two top entries (second / top) top = result, second = remainder

• cha' : duplicate top entry

• tam : swap top entries

• legh : view stack

• see : view stack in base 10

remember: ancient Klingon numbers only had the digits 1,2,3 and no ZERO.  The number NINE is not "30" (3x3 + 0), but 23 (2x3 + 3x1).

(This example  will perform (5 x 5) + 11 in Klingon.  Before doing the addition, the "see" command  will show the stack in base ten.  The final "." displays the result, "popping" the top of the stack for display.)

Klingon ArithmeticaL Kalculator:

try:

• 100 squared:   3131 cha' x .   (111123331)
• 2^2 + 3^3 + 4^4:    2 cha' x 3 cha' cha' x x + 11 cha' cha'  cha' x x x + .   (31122)

You can do this offline, using the Visual Basic program wKALK (pictured), or the console mode KALK program.  Both Windows binaries are included in the kalk.zip download file. NOTE: you will require the VBRUN300.DLL (not included) to run the Visual Basic program.

wKalk - a simple program to do Klingon arithmetic, using the 3 based number system.

The KALK.ZIP archive includes the console mode KALK.EXE, and the Visual Basic WKALK.EXE shown above.   Source for the KALK.EXE binary is also included.