Expressions to Truth-Tables

I had a need for the data in the truth tables for a standard cell library, rather like that shown here if you look at say page 35 you will see that for for every Cell it gives the cell name; the cell function as a boolean expression, and the truth-table for the cell.

My cell library was an Infineon one and I had the pdf version of the databook. A quick squirt through pdftotext scrambled the truth table, but did preserve the boolean expression of each cells' function, and the cell name.

I wrote a Python script that used a multi-line regexp to extract each cells info including the boolean equation.

The equation from the Infineon databook uses +,*, and ! for boolean or, and and not operators, but also used lots of parentheses so that operator precedence did not affect the value of the infix expression. I realised that I could substitute for the Python bitwise operators, and form a python expression that could then be evaluated with appropriate values for any input names to create a truth table.

I have left out the parsing and present a function to create a truth-table from a boolean expression:

from itertools import product

def truthtable(expressionstring):
  comp = compile(expressionstring.strip(), '-', 'eval')
  inputs = sorted(comp.co_names)
  table = {}
  for values in product( *([(0,1)] * len(inputs)) ):
      valuedict = dict(zip(inputs, values))
      answer = eval(comp, valuedict)
      table[values] = answer
  return expressionstring.strip(), inputs, table

def pptable(ex, inputs, table):
  print("\nTRUTH-TABLE FOR EXPRESSION: %r\n" % ex)
  print(' ' + ' '.join('%2s' % inp for inp in inputs) + ': OUTPUT')
  fmt = '  %i' * len(inputs) + ':  %i'
  for inp, ans in sorted(table.items()):
      print(fmt % tuple(list(inp) + [ans]))

ex, inputs, table = truthtable('(A & (~C)) | D')
pptable(ex, inputs, table)

Going through function truthtable:

• compile() gives access to all the names in the compiled expression via attribute .co_names - this is all the names used in the expression.
• product() allows you to quickly generate the 1/0 value combinations for the input names.
• valuedict assigns a value to each name used in the expression.
• eval evaluates the expression with the given values on each name

The output of the program is:

TRUTH-TABLE FOR EXPRESSION: '(A & (~C)) | D'

  A  C  D: OUTPUT
  0  0  0:  0
  0  0  1:  1
  0  1  0:  0
  0  1  1:  1
  1  0  0:  1
  1  0  1:  1
  1  1  0:  0
  1  1  1:  1

- No separate parser required!