Matrix Method to Detect Logic Hazards in Combinational Circuits with EX-OR Gates.pdf

Matrix Method to Detect Logic Hazards in Combinational Circuits with EX-OR Gates E. C. Tan (Nanyang Technological University, Singapore asectan@ntu.edu.sg) M. H. Ho (Nanyang Technological University, Singapore) Abstract: A matrix method is extended to include the detection of logic hazards in combinational logic circuits involving EX-OR gates. Essentially, the method generates 0- and 1-sets, or P- and S-sets, of all nodes in each gate level of a circuit progressively until it reaches the output of the circuit. The sets generated are subsequently used to determine the existence of static or dynamic hazards. Key Words: Hardware - Logic Hazards - Exclusive-OR Gates - Matrix Method 1 Introduction Hazards are unwanted switching transients which may appear at the output of a combinational circuit and are caused by propagation delays of the input signals. There are two types of hazards, viz., function and logic hazards, if we classify them by specific causes. A function hazard is associated with multiple-input changes while a logic hazard is caused by a single- input change. This paper will only deal with logic hazards. We can further classify hazards as being static or dynamic by their output waveforms. The presence of undesirable glitches at the output during the transition of two input states that have the same steady-state output is called a static hazard. It is a static 0 (1)-hazard if the steady-state output is 0 (1). Dynamic hazard occurs when the steady-state output values of two input states are different and the output experiences more than one change. The study of hazards in combinational logic circuits in the past [Beister 1974, McCluskey 1986, Tinder 1991, Almaini 1994, Wakerly 1994, Nelson et al. 1995] has mainly focused on logic elements other than exclusive-OR (EX-OR) gates. Comparing to the traditional AND/OR formulation of Boolean functions, the alternative AND/EX-OR logic approach based on Reed-Muller (RM) expansions [Green 1986, Almaini 1994] has adv