3 Data Selectors

3.3 Implementation of Digital Circuits using Memory

Several approaches exist to solve digital design problems. Some of those have been treated, so far.

Especially three methods can be distinguished because of their importance:

• The problem that should be solved is expressed algebraically in the form of a Boolean Function. The technical realization is done using special gate circuits. Circuits developed in this form have the advantage of a high execution speed, but they are more difficult to develop and to modify.
• The required output signals are generated out of the input signals using adequate data operations. The sequence of these operations are formulated in the form of algorithms and adjusted for special microprocessors and programmable circuits. When this method of circuit realization is applied, the required programs are usually stored in so-called read-only memories (ROMs). Intermediate values that are generated during the program execution are stored in read-write memory, known as random access memories (RAMs).
  Circuits implemented in this way are running more slowly, but they have the advantage of a more simple development and test phase.

When the Boolean Function is given, then the relation between input and output values is clearly defined, the circuit can be described in tabular form using a truth table. The most simple form to realize the circuit means just transferring the table to a memory device.

This leads directly to the method known as "Programmable Logic". The special circuits available for this purpose are summarized under the term PLD (programmable logic device).

Using the problem of BCD Code to 7-Segment Code conversion (see above), the memory-oriented solution can be explained. For this purpose the input variables representing the BCD-Code are interpreted as addresses of the memory device. The 7-segment code represents the memory content.

To store the complete table content in a memory device, obviously a memory capacity of 16 * 7 bits is needed.

The BCD-code is not complete. Therefore the input range for addresses 10 to 15 can be specified as "don't care" range, which in this case can be filled with '0' values.

Each of the seven Boolean Functions A - G of this table can be represented using a minterm decoding with subsequent OR-combination (see above).

Using memory address '2' and the output function 'E' this can be explained in detail:

To decode the input values (addresses) a simplified implementation is possible using an AND gate:

To describe the function E the minterms m0, m6, and m8 are also required. They can be implemented using equivalent decoder realizations (AND gates). Finally E can be formed using an OR-combination of all involved minterms:

.

(3.2)

Thus the relation of the memory-oriented presentation of the function to the minterm-representation treated before is established.

Solutions of this type using read-only memories (ROMs) have advantages and disadvantages:

Advantages:

• Circuits can be quickly implemented (important when building prototypes),
• Circuit realizations of this type are very cost-effective.

Disadvantages:

• The time to access the stored data and consequently the function is long (time to evaluate the decoders).
• The memory capacity is predefined. Therefore frequently not required information has to be defined:
  "don't care" positions are not possible.
• In this tabular solution neighbouring cells (fields) of identical content cannot be combined:
  Implicants cannot be formed.

Especially the fact that neither the introduction of "don't care" positions nor the formation of implicants are possible, can be considered a big drawback.