digi_notes - PHYS 331: Junior Physics Laboratory I Notes on...

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1 PHYS 331: Junior Physics Laboratory I Notes on Digital Circuits Digital circuits are collections of devices that perform logical operations on two logical states, represented by voltage levels. Standard operations such as AND, OR, INVERT, EQUIVALENT, etc. are performed by devices known as gates. Groups of compatible gates can be combined to make yes/no decisions based on the states of the inputs. For example, a simple warning light circuit might check several switch settings and produce a single yes/no output. More complicated circuits can be used to manipulate information in the form of decimal digits, alphanumeric characters, or groups of yes/no inputs. These notes are intended to familiarize you with the elementary principles of this field. A. Analysis of asynchronous logic Suppose we have a statement which can be true or false, perhaps representing the presence or absence of a particle, a light signal on or off, a voltage present or absent, or any other binary possibility. For now we will ignore the physical meaning of the statement and ask how one would decide the logical truth or falsehood of combinations of such statements, a subject called combinatoric logic. If we denote the "truth value" of a statement A by 0 or 1, the standard combinations are shown in the form of "truth tables" in Fig. 1. These basic combinations, or A B Q 0 0 0 0 1 0 1 0 0 1 1 1 AND A B Q A B Q 0 0 0 0 1 1 1 0 1 1 1 1 OR A B Q A A Q 0 1 1 0 NOT A B Q 0 0 1 0 1 1 1 0 1 1 1 0 NAND A B Q A B Q 0 0 1 0 1 0 1 0 0 1 1 0 NOR A B Q A B Q 0 0 0 0 1 1 1 0 1 1 1 0 XOR A B Q Q Fig. 1 Standard logic symbols and truth tables.
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2 similar ones, have been implemented in electronic circuitry, where truth values can be represented by different voltage levels. The standard circuit symbols are also shown in Fig. 1. By combining the basic operations we can construct other logical functions. For example, suppose we wish to determine whether or not a particle has stopped in a target, using the configuration of counters shown in Fig. 2. A particle passing through a counter makes the corresponding output true, and we assume the particle has stopped in the target if A and B are both true, but C is false. Formally, we want to know when the compound statement A B C is true. An electronic implementation of the compound statement is also shown in Fig. 2, together with a truth table. Examination of the truth table shows that A B C is true in exactly one situation, which corresponds to the physically desired result. Sometimes it is not obvious how to write down the required expression and implement it. You might discover an implementation using only standard operations by trial and error, but it is possible to be more systematic. For example, suppose we wish to make an exclusive-OR function using AND, OR and NOT gates. To do this we can try to combine some statements that are true for exactly one combination of A and B . Consider the following: A B is true only when A = 1 and B = 1 A B is true only when A = 1 and B = 0 (1) A B is true only when A = 0 and B = 1 A
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digi_notes - PHYS 331: Junior Physics Laboratory I Notes on...

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