Christian-Albrechts-Universität zu Kiel
Institut für Informatik
Lehrstuhl für Technische Informatik
Prof.Dr. Manfred Schimmler
Dr.-Ing. Christoph Starke, M.Sc. Sven Koschnicke
Digital Systems
Wintersemester 2014/2015
Serie 3
Assignment Date: Wednesday, 12.11.2013
Date of submission: Monday, 24.11.2013, 8 o’clock
Presentation tasks
Task 1
Show for a Boolean algebra: (A, +, ·) : ∀x0 , x1 ∈ A : (x0 + x1 ) · (x0 + x1 ) = x0
Make use of the theorems and axioms on Boolean algebra in the lectures slides.
Task 2
(a) Determine the canonical disjunctive normal form of
f = (x2 x0 + x2 x1 + x2 x0 ) · (x0 + x1 ) · (x2 x1 + x2 x1 )
(b) Represent the minimized solution of a) as a combinatorial circuit.
Task 3
Minimize the following funtion using the Karnaugh map (in German: KV-Diagramm):
f = x2 x1 x0 + x2 x1 x0 + x2 x1 x0 + x2 x1 x0 + x2 x1 x0
Homework
Task 1
Show for a Boolean algebra: (A, +, ·) :
(a) ∀x0 , x1 ∈ A : x0 · x1 + (x0 + x1 ) = 1
(b) ∀x0 , x1 ∈ A : x0 + x1 = x0 · x1
Make use of the theorems and axioms on Boolean algebra in the lectures slides (without
the theorem to be proven).
10, 20 points
Version November 10, 2014
Page 1 of 2
Task 2
(a) Determine the canonical disjunctive normal form of
f1 = (x2 x0 + x1 x0 ) · (x1 + x2 x0 ) · (x2 x1 x0 + x1 x0 + x2 x1 )
(b) Determine the canonical conjunctive normal form of
f2 = x3 x2 x1 + x3 x2 x0 + x3 x1 x0 + x3 x2 x1 x0
(c) Represent the minimized solutions of a) and b) as a combinatorial circuit.
10, 10, 20 points
Task 3
Minimize the following functions to the disjunctive minimal form (DMF) using the Karnaugh map:
(a) f1 = x2 x1 x0 + x2 x1 x0 + x2 x1 x0 + x2 x1 x0 + x2 x1 x0
(b) f2 = x3 x2 x1 x0 +x3 x2 x1 x0 +x3 x2 x1 x0 +x3 x2 x1 x0 +x3 x2 x1 x0 +x3 x2 x1 x0 +x3 x2 x1 x0 +x3 x2 x1 x0
10, 20 points
Version November 10, 2014
Page 2 of 2