LogicMin: Logic Minimization in Python

Minimize logic functions.

Description

LogicMin is a Python package that minimize boolean functions using the tabular method of minimization (Quine-McCluskey). An object represent a truth table to which rows are added. After all rows are added, call a solve function.The solve function returns the minimized Sum of Products. The sum of products can be printed or analyzed.

For more information, look into references:

- Edward J. McCluskey. 1986. Logic Design Principles with Emphasis on Testable Semicustom Circuits. Prentice-Hall, Inc., Upper Saddle River, NJ, USA. 
- John F. Wakerly. 1989. Digital Design Principles and Practices. Prentice-Hall, Inc., Upper Saddle River, NJ, USA.

Full-adder

	# Full-adder
	import logicmin
	# truth table 3 inputs, 2 outputs
	t = logicmin.TT(3,2);
	# add rows to the truth table (input, ouutput)
	# ci a b  |  s co
	t.add("000","00")
	t.add("001","10")
	t.add("010","10")
	t.add("011","01")
	t.add("100","10")
	t.add("101","01")
	t.add("110","01")
	t.add("111","11")
	# minimize functions and get
	# solution for analysis and print
	sols = t.solve()
	# print solution mapped to var names (xnames=inputs, ynames=outputs)
	# add debug information
	print(sols.printN(xnames=['Ci','a','b'],ynames=['s','Co'], info=True))

Output:

	Co <= a.b + Ci.b + Ci.a
	s <= Ci'.a'.b + Ci'.a.b' + Ci.a'.b' + Ci.a.b

Get expression in VHDL syntax:

	print(sols.printN(xnames=['Ci','a','b'],ynames=['s','Co'], syntax='VHDL'))

Output:

	Co <= a and b or Ci and b or Ci and a
	s <=  not(Ci) and  not(a) and b or  not(Ci) and a and  not(b) or Ci and  not(a) and  not(b) or Ci and a and b

BCD to 7 segment converter

	# BCD-8421 to 7 segment
	import logicmin
	t = logicmin.TT(4,7);
	# b3 b2 b1 b0  | a b c d e f g 
	t.add("0000","1111110") 
	t.add("0001","0110000") 
	t.add("0010","1101101") 
	t.add("0011","1111001") 
	t.add("0100","0110011") 
	t.add("0101","1011011") 
	t.add("0110","0011111") 
	t.add("0111","1110000") 
	t.add("1000","1111111") 
	t.add("1001","1110011") 
	t.add("1010","-------") 
	t.add("1011","-------") 
	t.add("1100","-------") 
	t.add("1101","-------") 
	t.add("1110","-------") 
	t.add("1111","-------") 
	# Outputs minimized independently
	sols = t.solve()
	print(sols.printN( xnames=['b3','b2','b1','b0'], ynames=['a','b','c','d','e','f','g']))

Output:

	g <= b2'.b1 + b2.b1' + b2.b0' + b3
	f <= b1'.b0' + b2.b1' + b2.b0' + b3
	e <= b2'.b0' + b1.b0'
	d <= b2.b1'.b0 + b2'.b0' + b2'.b1 + b1.b0'
	c <= b1' + b0 + b2
	b <= b1'.b0' + b1.b0 + b2'
	a <= b2'.b0' + b1.b0 + b2.b0 + b3

Finite-state machines

For finite-state machines, a FSM object is provided.

The advantages of FSM objects are:

1. States can have meaningful names.
2. It is possible to try different state code assignments to evaluate result complexity. 

Binary counter with hold

	# Finite-state machine
	# x=0 => hold
	# x=1 => binary up count
	# y = 1 in states: e1 and e3
	import logicmin
	# state labels
	states = ['e0','e1','e2','e3']
	# 2 bits for state codes
	# 1 input variable
	# 1 output variable
	m = logicmin.FSM(states,2,1,1)
	# transition table
	m.add('0','e0','e0','0')
	m.add('1','e0','e1','0')
	m.add('0','e1','e1','1')
	m.add('1','e1','e2','1')
	m.add('0','e2','e2','0')
	m.add('1','e2','e3','0')
	m.add('0','e3','e3','1')
	m.add('1','e3','e0','1')
	# asign code to states
	codes = {'e0':0,'e1':1,'e2':2,'e3':3}
	m.assignCodes(codes)
	# solve with D flip-flops
	sols = m.solveD()
	# print solution with input and output names
	print(sols.printN(xnames=['X','Q1','Q0'], ynames=['D1','D0','Y']))

Output:

	Y <= Q0
	D0 <= X'.Q0 + X.Q0'
	D1 <= X.Q1'.Q0 + X'.Q1 + Q1.Q0'

Other examples

Look into examples directory.

Install

 	pip install logicmin