Fundamentals - The MPEG - page 39

implement virtually any process. Figure 2.30 shows that the first type is a logic element. This produces an output
which is a logical function of the input with minimal delay. The second type is a storage element which samples the
state of the input(s) when clocked and holds or delays that state.
Figure 2.30: Logic elements have a finite propagation delay between input and output and cascading them delays
the signal an arbitrary amount. Storage elements sample the input on a clock edge and can return a signal to near
coincidence with the system clock. This is known as reclocking. Reclocking eliminates variations in propagation
delay in logic elements.
The strength of binary logic is that the signal has only two states, and considerable noise and distortion of the
binary waveform can be tolerated before the state becomes uncertain. At every logical element, the signal is
compared with a threshold, and can thus can pass through any number of stages without being degraded. In
addition, the use of a storage element at regular locations throughout logic circuits eliminates time variations or
jitter. Figure 2.30 shows that if the inputs to a logic element change, the output will not change until the propagation
delay of the element has elapsed. However, if the output of the logic element forms the input to a storage element,
the output of that element will not change until the input is sampled at the next clock edge . In this way the signal
edge is aligned to the system clock and the propagation delay of the logic becomes irrelevant. The process is
known as reclocking.
2.15 Logic elements
The two states of the signal when measured with an oscilloscope are simply two voltages, usually referred to as
high and low. The actual voltage levels will depend on the type of logic family in use, and on the supply voltage
used. Supply voltages have tended to fall as designers seek to reduce power consumption. Within logic, the exact
levels are not of much consequence, and it is only necessary to know them when interfacing between different
logic families or when driving external devices. The pure logic designer is not interested at all in these voltages,
only in their meaning.
Just as the electrical waveform from a microphone represents sound velocity, so the waveform in a logic circuit
represents the truth of some statement. As there are only two states, there can only be true or false meanings. The
true state of the signal can be assigned by the designer to either voltage state. When a high voltage represents a
true logic condition and a low voltage represents a false condition, the system is known as positive logic , or high
true logic. This is the usual system, but sometimes the low voltage represents the true condition and the high
voltage represents the false condition. This is known as negative logic or low true logic. Provided that everyone is
aware of the logic convention in use, both work equally well.
In logic systems, all logical functions, however complex, can be configured from combinations of a few fundamental
logic elements or gates . It is not profitable to spend too much time debating which are the truly fundamental ones,
since most can be made from combinations of others. Figure 2.31 shows the important simple gates and their
derivatives, and introduces the logical expressions to describe them, which can be compared with the truth-table
notation. The figure also shows the important fact that when negative logic is used, the OR gate function
interchanges with that of the AND gate.