Computer Arithmetic - Design and Verification - Sommersemester 2026
Übersicht
| Beschreibung |
The lecture covers fundamental approaches to computer arithmetic and to the verification of arithmetic circuits. The availability of fast implementations of arithmetic functions is essential for numerous areas of computer science, mathematics, and various natural sciences. Due to increasing miniaturization, unlike early CPUs, todays processors usually have sufficient area available to implement complex arithmetic functions in hardware and to utilise fast hardware with relatively high area requirements. The lecture first covers the fundamentals of computer arithmetic, including different number systems (for unsigned and signed integers as well as floating-point numbers). Then it presents various architectures for implementing basic arithmetic operations, such as addition, multiplication, and division, together with estimates of their complexity. The use of implementations of arithmetic functions, especially in safety-critical areas, requires them to be correct. Since arithmetic circuits place special demands on verification, the lecture covers special methods for the fully automatic formal verification of arithmetic circuits. After introducing suitable data structures for verification, such as binary decision diagrams (BDDs), functional decision diagrams (FDDs), binary moment diagrams (BMDs), and polynomials over integers - including the corresponding mathematical foundations - the lecture deals with the verification of different classes of arithmetic circuits. Recommended (not mandatory) requirements: Familiarity with basic computer engineering concepts, such as Boolean algebra and fundamentals of circuit design, is required for the lecture and the exercises. Course material will by shared via ILIAS (link follows). |
| Kommentar |
Specialization course, ESE, Computer Science, 3+1 ECTS: 6 |