Driving method of driving a liquid crystal display element

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The present invention relates to a method of driving a liquid crystal display element to display fast moving images.

In recent years, liquid crystal display elements have been noted as devices which are thin, light, compact and capable of displaying a large capacity of information, in place of CRTs. As driving methods to such liquid crystal display elements, they are mainly classified into two methods wherein each picture element of a twisted nematic type liquid crystal display element is driven by a thin-film transistor which is disposed in correspondence to each of the picture elements, and a twisted nematic type or a super-twisted nematic type liquid crystal display element is driven without using a thin-film transistor (a simple matrix type).

Although the liquid crystal display element with a thin film transistor can be driven at a relatively high speed, there is a problem that manufacturing steps for preparing the element are complicated and manufacturing cost is high. On the other hand, although manufacturing steps for the simple matrix type liquid crystal display element are relatively simple, there is a problem that it is difficult to switch a display picture at a high speed, whereby it is difficult to obtain a quick response in a display with a mouse at a terminal device when displaying video images.

The reason why it is difficult to drive the simple matrix type liquid crystal display element satisfactorily at a high speed is because the time required for orienting the liquid crystal molecules is large when a voltage is applied to the liquid crystal, which is inherent in the characteristics of the twisted nematic type or the super-twisted nematic type liquid crystal display element. Namely, in such liquid crystal display element having an average response time of about 250 msec, it is impossible to switch a display element or pixel at 20 Hz-30 Hz (which corresponds to a switching time of 33-50 msec) which is generally required in video display.

For high-speed driving, it is considered to use a liquid crystal element having a low response time to a voltage applied to liquid crystal. Such liquid crystal element is called a fast response type liquid crystal element. In order to obtain such fast response type liquid crystal element, there are such a method of using liquid crystal having a low viscosity and such a method that the thickness of the liquid crystal layer is reduced by using liquid crystal having a large refractive index anisotropy.

The response time of the super-twisted nematic type liquid crystal display element is generally in proportion to the viscosity .eta. of the liquid crystal used and is in proportion to the square of the thickness d of the liquid crystal layer used. On the other hand, in consideration of the demand that the product of the refractive index anisotropy .DELTA.n of the super-twisted nematic type liquid crystal display element and the thickness d of the liquid crystal layer should be substantially constant, the response time of the liquid crystal display element is in proportion to the viscosity .eta. and is in inverse proportion to the square of the refractive index anisotropy .DELTA.n. Namely, it is preferable that the thickness d of the liquid crystal layer is small, and liquid crystal having a low viscosity and a large refractive index anisotropy is used for the liquid crystal element.

However, even though a fast response type liquid crystal element can be obtained in a manner as described above, use of such element has encountered an extremely large problem, which is described below. Generally, a method called optimized amplitude selective addressing method (e.g. "LIQUID CRYSTAL TV DISPLAYS" by E. Kaneko, 1987, published by KTK Scientific Publishers) has been used for driving a simple matrix type liquid crystal display element. In the waveform of a voltage applied to line electrodes in the optimized amplitude selective addressing method wherein the number of scanning lines (the number of row electrodes) is N and the frame period is T.sub.F, there is a single selection pulse in the frame period T and a bias wave having a amplitude, which is 1/b as high as an ON voltage selection pulse, in a time other than the application of the selection pulse. Namely, a time of T.sub.F /N is assigned to in a selection time period and a time of (N-1)T.sub.F /N is assigned to a non-selection time period. In FIG. 5a, a symbol A shows a typical waveform of a voltage applied, wherein the abscissa represents time and the ordinate represents voltage. In many cases, two frames are used so as to form an a.c. voltage (d.c. free operation).

In the optimized amplitude selective addressing method, the response characteristic of liquid crystal molecules is effected by the r.m.s. value of the applied voltage to thereby be obtainable a predetermined contrast ratio of display. In FIG. 5b, a symbol C shows a curve of effective value to which the liquid crystal molecules are responsive to the applied voltage wherein the abscissa represents time and the ordinate represents the intensity of transmitting light in a case that polarization plates are arranged at both sides of the liquid crystal layer and an ON voltage is applied to the column electrodes at the time of selection of the line electrodes. Generally, a frame period of about 10 msec-several 10 msec is used, whereas the average response time of a normally used liquid crystal display element is about 250 msec. Accordingly, switching a single pixel of ON or OFF is completed by using several numbers of frames through ten and several numbers of frames.

When a fast response type liquid crystal display element is driven, a change in the direction of the axis of the liquid crystal molecules is apt to follow to the amplitude of voltage applied to the liquid crystal. Accordingly, the transmission of light through the cell as indicated by a wave B in FIG. 5b, the liquid crystal molecules are responsive to peak values, which does not follow the curve C of the integrating responsive characteristic. Namely, there causes a problem that the optical transmission through the cell which rises in a selection time period attenuates in a non-selection time period, whereby the average transmittance level decreases and hence the contrast ratio also decreases. Hereinafter, such phenomenon is called the "relaxation" of liquid crystal.

The relaxation phenomenon causes a serious problem when the number of rows multiplexed (N) is several hundreds or more and a liquid crystal display element having a average response time of about 150 msec or lower is used. In particular, it is considerable when the multiplexing is conducted to a liquid crystal display element having a average response time of about 100 msec or lower.

In this specification, the average response time of a liquid crystal display element is defined as follows.

When a light transmission degree on the application of an OFF voltage at the time when a sufficient time has passed is represented as T.sub.OFF, a light transmission degree on the application of an ON voltage is as T.sub.ON, the time of switching from the OFF voltage to the ON voltage is as t.sub.1, the time when the light transmittance degree T becomes (T.sub.ON -T.sub.OFF).times.0.9+T.sub.OFF after the switching time is T.sub.2, the time of switching from the ON voltage to the OFF voltage again is as t.sub.3, and the time when the light transmission degree T becomes (T.sub.ON -T.sub.OFF).times.0.1+T.sub.OFF after the second switching time is as t.sub.4, the average response time .tau. is expressed as follows:

.tau.=((t.sub.4 -t.sub.3)+(t.sub.2 -t.sub.1))/2

In order to suppress the relaxation phenomenon, it is considered to utilize a method of increasing the frame frequency to thereby shorten time intervals between selection pulses. In this case, however, a time to select a single line electrode (a pulse width) is necessarily short, and therefore, the reaction of the liquid crystal molecules to the selection pulses is delayed. Accordingly, effect of increasing the contrast ratio of a display is not large.

Further, when the magnitude of a frequency for driving is large, the resistance value of the electrodes is not negligible, so that there causes brightness nonuniformity in a display between a signal inputting portion of an electrode and the other portion, or there causes brightness nonuniformity in a display because of a change of V.sub.th with frequency. For the above-mentioned reasons, it was difficult to use the fast response type liquid crystal display element for the purpose of displaying good images.

On the other hand, T. N. Ruckmongathan proposes a method called Improved Hybrid Addressing Technique wherein a plurality of row electrodes are selected simultaneously or as a batch to drive them (hereinafter, referred to as IHAT method) in order to reduce a driving voltage and to minimize brightness nonuniformity in a display (1988 Internal Display Research Conference). A summary of the driving method is as follows.

An N number of line electrodes are divided into a p number (p=N/M) of subgroups each consisting of an M number of line electrodes, and the M number of line electrodes are selected as a batch to drive them.

A display information of an optional row of column electrodes in a selected subgroup is represented by an M-bit code [d.sub.KM+1, d.sub.KM+2, . . . , d.sub.KM+M ]; d.sub.KM+j= 0 or 1 (where 0 designates OFF and 1 designates ON, and k is an integer changeable from 0 to (p-1) in a selected subgroup).

A selection pattern for the line electrodes is expressed by M-bit code (W.sub.1, W.sub.2, . . . , W.sub.Q) of 2.sup.M (=Q) kinds, i.e., [a.sub.KM+1, a.sub.KM+2, . . . , a.sub.KM+M ]; a.sub.KM+j =0 or 1.

The driving is conducted as follows.

(1) A subgroup is selected as a batch.

(2) An M-bit code is selected as a selection pattern for the line electrodes.

(3) When the line electrodes which are not selected are connected to the ground, the line electrodes selected are applied with -V.sub.r for logic 0 and +V.sub.r for logic 1.

(4) A line electrode pattern for the selected subgroup and a data pattern are compared for each bit by using exclusive logical sum (exclusive OR) to thereby obtain a value of the exclusive logical sum of these data.

(5) A mismatch number i of the two patterns is obtained from the exclusive logical sum.

(6) When the mismatched number is i, a voltage applied to the column electrodes is selected to be V.sub.i.

(7) The voltage applied to the column electrodes is determined independently by repeating the steps (4)-(6) in the matrix.

(8) The voltage is applied to the line electrodes and the column electrodes simultaneously during a time T.sub.R.

(9) A selection pattern is newly selected for the line electrodes, and a voltage applied to the column electrodes is determined through the steps (4)-(6). In the same manner as above, the voltage is applied simultaneously to another line electrodes and column electrodes during a time T.sub.R.

(10) A cycle is completed when a 2.sup.M number of selection patterns are selected once for all subgroups.

(11) A display is refreshed by repeating continuously the cycle.

In particular, when equations:

V.sub.i =V.sub.0 (M-2i)/M, and

V.sub.r =V.sub.0 N.sup.1/2 /M

are selected, the ON/OFF ratio of root mean square (r.m.s.) value of voltage can be largest. In this case, the ratio of the root mean square voltage of ON and OFF is expressed by:

V.sub.ON /V.sub.OFF =((N.sup.1/2 +1)/(N.sup.1/2 -1)).sup.1/2

The value obtainable is equal to V.sub.ON /V.sub.OFF which is obtainable by using the conventional optimized amplitude selection method. Further, the effective value of voltage at each operating portion in the matrix becomes uniform, whereby a uniform display can be obtained regardless of display patterns.

While the IHAT is effective for reducing the brightness nonuniformity of display, the number of time intervals to complete a cycle is long and hence is not suitable for gray shades using a technique similar to frame modulation. In this case, when the number of row electrodes selected is increased, the number of selection pulses required is sometimes increased as an exponential function. If the width of a selection pulse is uniform, a display requires a time 2.sup.M-1 /M times as much as the conventional method. For instance, if M=7, then 64/7, i.e. a time of 9.1 times is required.

It is an object of the present invention to eliminate the problems of the conventional driving method and to provide a new driving method for a liquid crystal display element.

In accordance with the present invention, there is provided a driving method of a matrix type liquid crystal display element comprising at least J.times.L number (J and L are respectively integers of 2 or more) of row electrodes and a plural number of column electrodes wherein,

said J.times.L number of row electrodes are divided into a J number of row electrode subgroups each comprising an L number of row electrodes so that said subgroups are selected as each batch to be driven;

when voltages are applied to the row electrodes, either a voltage level of +V.sub.r or -V.sub.r (where V.sub.r >0) is applied at a selection time, when a voltage at a non-selection time is 0 (zero);

voltages applied to the column electrodes are selected from an (L+1) number of voltage levels of V.sub.0, V.sub.1, . . . , V.sub.L (where V.sub.0 <V.sub.1 <. . . <V.sub.L); and

when a two-valued information of the j-th row electrode subgroup (j is an integer of any of 1 through J) in a specified column in the plural column electrodes is expressed by a column vector D.sub.j having an L number of elements (where the elements of the vector D.sub.j comprises 1 indicating ON and 0 indicating OFF), the following conditions are satisfied:

(1) said j-th row electrode subgroup is selected by applying sequentially voltages so that the elements of a selection voltage vector which constitute a row selection voltage, as defined in the following items (a) and (b), correspond to voltages to the row electrodes constituting the j-th line electrode subgroups:

(a) an orthogonal matrix A=[.alpha..sub.1, .alpha..sub.2, . . . , .alpha..sub.q, . . . , .alpha..sub.k ] (where .alpha..sub.q is a column vector having an L number of elements) comprising L rows and K columns, which has an element of +V.sub.r or -V.sub.r and in which the product of a matrix and a transposed matrix of the same assumes a scalar multiple of the unit matrix is selected (where K is an integer having a relation of L.ltoreq.2.sup.p =K and p is a natural number), and

(b) as said row selection voltage, a selection voltage vector which includes at least one of .alpha..sub.1, .alpha..sub.2, . . . , .alpha..sub.k, -.alpha..sub.1, -.alpha..sub.2, . . . , -.alpha..sub.k is selected, and, (2) when said j-th row electrode subgroup is selected under the above-condition (1), the voltage applied to the column electrodes to indicate a display information by means of the vector D.sub.j are determined as in the following items (a) and (b):

(a) a vector .beta. is formed by the selection voltages applied to the j-th row electrode subgroup where +V.sub.r represents 1 and -V.sub.r represents 0, and

(b) a voltage V.sub.i (i is an integer of any of 0 through L) given by the sum of exclusive OR of the elements corresponding to the vector .beta. and D.sub.j is applied to the column electrodes.

Further, it is an object of the present invention to provide a driving method of liquid crystal display element as described in the above wherein the display information of the j-th row electrode subgroup in a specified column of the plural column electrodes has a gradation of (U+1) stages (where U is a natural number of 2 or more) in place of the two-valued information;

the selection vectors which constitute a row selection voltage comprise substantially each U number of .alpha..sub.1, .alpha..sub.2, . . . , .alpha..sub.k, -.alpha..sub.1, -.alpha..sub.2, . . . , -.alpha..sub.k in which the selection voltage vectors are arranged in a row, are selected, and the selected vectors having the each U number are used to display a gradation display of (U+1) stages by giving a specified ratio to the total U number of ON and OFF signs.

In drawings:

FIG. 1(a-d) is a graph showing time sequential changes of electric potential of a row electrode subgroup comprising R.sub.1 -R.sub.4 in a case of applying the selection code shown in Table 1;

FIG. 2 is a diagram showing a display pattern for a liquid crystal display element;

FIG. 3 is a graph showing changes of voltages applied to column electrodes C.sub.1, C.sub.2, C.sub.3, C.sub.9 with the display pattern shown in FIG. 2 in a case of applying the selection code shown in Table 1;

FIG. 4 is graphs showing voltages applied to the electrodes R.sub.1 -C.sub.9 and R.sub.2 -C.sub.9 with the display pattern of FIG. 2 in a case of applying the selection code shown in Table 1;

FIG. 5(a-b) is graphs showing an integrating response characteristic and a relaxation phenomenon;

FIG. 6 is a block diagram showing an example of a circuit for realizing the driving method of the present invention;

FIG. 7 is graphs showing time sequential changes of voltages of a row electrode subgroup comprising R.sub.1 -R.sub.4 in a case of applying the selection code shown in Table 4;

FIG. 8 is graphs showing time sequential changes of voltages of a row electrode subgroup comprising R.sub.1 -R.sub.3 in a case of applying the selection code shown in Table 6;

FIG. 9 is graphs showing voltages applied to column electrodes C.sub.1, C.sub.2, C.sub.3, C.sub.9 with the display pattern of FIG. 2 in a case of applying the selection code shown in Table 4;

FIG. 10 is graphs showing voltages applied to the electrodes R.sub.1 -C.sub.9 and R.sub.2 -C.sub.9 with the display pattern of FIG. 2 in a case of applying the selection code shown in Table 4;

FIG. 11 is graphs showing voltage waveforms applied to column electrodes with display patterns in a case of applying selection code shown in Table 6;

FIG. 12 is graphs showing waveforms of the difference of electric potential between the electrode R.sub.3 shown in FIG. 8 and an optional column electrode in cases of the entirely ON and OFF;

FIG. 13 is a block diagram showing an example of a circuit for realizing the driving method of the present invention;

FIG. 14 is a graph showing changes of the contrast ratios according to a conventional method and the present invention wherein the width of a selection pulse is changed; and

FIG. 15 is an another graph showing changes of the contrast ratios in accordance with conventional method and the present invention wherein the width of a selection pulse is changed.

In the following, several embodiments of the present invention will be described in detail with reference to the drawings.

In the driving method according to the present invention, a plurality of row electrodes are selected as a batch in the same manner as the IHAT method. In this description, a group of row electrodes selected as a batch is called "a row electrode subgroup".

It is desirable that the number of row electrodes which constitute each of the row electrode subgroups is equal in order to simplify a driving circuit. However, since, in the construction of a typical cell, the total number of row electrodes is not equal to a multiple number of the row electrodes which constitute row electrode subgroups, it is sometimes impossible that the number of the row electrodes which constitute all row electrode subgroups is equal.

A case of driving row electrode subgroups each having an L number of row electrodes will be described (a case of driving row electrode subgroups in which some of row electrode subgroups have a fraction number of row electrodes will be also described).

In dividing the row electrodes into several row electrode subgroups, it is not always necessary to select adjacent row electrodes as a row electrode subgroup, but it is possible to select row electrodes at a position apart from another electrodes as a row electrode subgroup as far as there is no problem of wiring on a substrate.

In the present invention, it is preferable to use a fast response type liquid crystal display element. As described before, such fast response type liquid crystal display element can be obtained by reducing the thickness (d) of the liquid crystal layer and by using liquid crystal having a low viscosity and a large anisotropy of refractive index. As the liquid crystal having a large anisotropy of refractive index, a tolan type liquid crystal component is useful, such tolan type liquid crystal component being disclosed in, for instance, Japanese Unexamined Patent Publication No. 5631/1986. Further, there are liquid crystal having features as shown in Chemical Formulas 1. ##STR1##

In the above chemical formulas, --X-- is --COO--, --OCO--, --CH.sub.2 CH.sub.2 -- or --C.tbd.C--; and R.sup.1 and R.sup.2 are independently a C.sub.1 -C.sub.10 alkyl group, a halogen atom, a cyano group or a --SCN group, provided that when R.sup.1 and R.sup.2 have a carbon-carbon bond, an oxygen atom may be inserted between the carbon-carbon bond or between the carbon and an adjacent ring, or a part of the carbon-carbon bonds may be substituted by --COO--, --OCO-- or --CH.dbd.CH--. These compounds are simply for illustration, but there may optionally be selected various other materials, the hydrogen atom of which may be substituted by a halogen atom, a cyano group, a methyl group or the like.

Further, as material having a large anisotropy of refractive index and a low viscosity, a difluorostilbene type liquid crystal is useful. As the difluorostilbene type liquid crystal, there are such liquid crystal components described in, for instance, Japanese Unexamined Patent Publication No. 96475/1989. Further, there are chemical structures shown in Chemical Formulas 2. ##STR2##

In the above chemical formulas, --X-- is --COO--, --OCO--, --CH.sub.2 CH.sub.2 -- or --C.tbd.C--; and R.sup.1 and R.sup.2 are independently a C.sub.1 -C.sub.10 alkyl group, a halogen atom, a --CN group or a --SCN group, provided that when R.sup.1 and R.sup.2 have a carbon-carbon bond, an oxygen atom may be inserted between the carbon-carbon bond or between the carbon and an adjacent ring, or a part of the carbon-carbon bonds may be substituted by --COO--, --OCO-- or --CH.dbd.CH--. These compounds are simply for illustration, but there may optionally be selected various other materials, the hydrogen atom of which may be substituted by a halogen atom, a cyano group, a methyl group or the like.

The difluorostilbene type and the tolan type liquid crystal materials may be used separately or simultaneously. In particular, a liquid crystal composition containing 1-80% by weight of difluorostilbene, preferably 5-70% by weight, more preferably 10-60% by weight can greatly reduce the viscosity and can realize a fast response.

In the present invention, voltages to be applied to line electrodes are either a voltage level of +V.sub.r or -V.sub.r (V.sub.r >0) in an selection time wherein voltages in a nonselection time is 0. In this case, the voltage of 0 in a non-selection time does not always mean grounding to the earth. A driving voltage to a liquid crystal element is determined by a voltage (a potential difference) applied between a line electrode and a column electrode. It is because a potential difference between the both electrodes is not changed by changing the potential of the both electrodes by the same quantity in parallel.

The voltages applied to a specified row electrode subgroup in a selection time can be expressed by vectors with L elements which are arranged time sequentially, the vectors having, as elements, voltages applied to each row electrodes. In this description, such matrices are called "selection voltage matrices", and the vectors which constitute the row select voltages are called "selection voltage vectors". Namely, if specified selection voltage matrices are determined, it is possible to select a row electrode subgroup in such a manner that the elements of the selection vectors which constitute the selection voltage matrices are made in correspondence to the voltages for each row electrodes, and the voltages corresponding to the selection voltage vectors which constitute the selection voltage matrices are sequentially applied to the row electrodes.

In the following, description will be made as to a method of forming the selection voltage matrices according to the present invention.

First of all, a matrix A of L rows and K columns: A=[.alpha..sub.1, .alpha..sub.2, . . . , .alpha..sub.q, . . . , .alpha..sub.K ] (where .alpha..sub.q is a column vector having an L number of elements) which has an element of +V.sub.r or -V.sub.r and in which the product of a matrix and a transposed matrix of the same assumes a scalar multiple of the unit matrix, is selected. In the matrix, K is an integer having a relation of L.ltoreq.2.sup.p =K, where p is a natural number. Describing specifically some examples, when L is 2, K is such that K=2(p=1), (p=2), 8(p=3), . . . . When L is 3 or 4, K assumes K=4, 8, 16, . . . . Further, when L is 5, 6, 7 or 8, K assumes K =8, 16, 32, . . . . However, when K is too large, the number of selection pulses necessary for the selection of line electrodes is also large. Accordingly, it is preferable that K assumes the smallest value among possible values.

Examples of the matrix A in which L =4, 8 and K =4, respectively, are shown in the following Lists 1. ##STR3##

As a result of practicing several kinds of matrices, and especially when the matrices described in the above Lists 1(a) and (c) which are called an Hadamard's matrix were used, it was found that an advantage was obtainable in reducing the brightness nonuniformity of display when liquid crystal elements were driven. In the case of L.noteq.2.sup.p, the above-mentioned L-lines-K columns matrix A can be formed by removing an optional (K-L) line from a K-rows matrix wherein the product of a matrix and a transposed matrix of the same forms a scalar multiple of the unit matrix. The following Lists 2 show examples of the martix A transformed from the 8-dimensional Hadamard's matrix shown in List 1(c), for instance. ##STR4##

List 2(a) shows a 7-row-8-column matrix formed by removing the first row from the matrix shown in List 1(c), and List 2 (b) is a 6-row-8-column matrix formed by removing the first and eighth rows from the matrix shown in List 1(c). In each of the matrices, the product of a matrix and a transposed matrix of the same assumes a scalar multiple of the unit matrix.

In the matrix A, each of the columns can be considered to be a single vector, whereby a formal expression of A=[.alpha..sub.1, .alpha..sub.2, . . . , .alpha..sub.q, . . . , .alpha..sub.k ] (where .alpha..sub.q is a column vector having an L number of elements) is made.

In the present invention, as the selection voltage matrices, matrices of vectors wherein the selection voltage vectors constituting the selection voltages are composed of at least .alpha..sub.1, .alpha..sub.2, . . . .alpha..sub.K, -.alpha..sub.1, -.alpha..sub.2, . . . , -.alpha..sub.K, and these selection voltage vectors are arranged in matrices are selected.

If two values (i.e. ON and OFF) are used for displaying information to be described, selection voltage matrices consisting of a 2K number of vectors wherein each of the vectors appears once in the selected voltage matrices can be selected.

However, it is not always necessary that the selection voltage matrices are formed by selecting each one among the 2K number of vectors, but it is possible to add another vector composed of +V.sub.r or -V.sub.r as an element, or an arrangement of a plurality of same vectors as far as effect by the present invention is not adversely affected. For instance, an arrangement of selection voltage matrices including all possible conditions of electric potential (in this case, the number of selection voltage vectors in the selection voltage matrices is 2.sup.L or higher) can be considered. For instance, if a single row electrode subgroup is formed of four row electrodes, there are 16 kinds of possible conditions of electric potential (2.sup.4 =16). Namely, selection voltage matrix include 16 selection voltage vectors. Accordingly, the voltages corresponding to the selection voltage matrix form a row electrode selection waveform for the driving method of the present invention.

In the above method, each of the row electrode subgroups has all possible electric potential conditions, whereby brightness nonuniformity in a display can be effectively reduced. However, when the value L becomes large, the number of selection pulses required for the selection of row electrodes increases in a form of exponential function, and if the pulse width is unchanged, a time required for completing a single display cycle becomes extremely long. In this sense, it is most preferable to select selection voltage matrices wherein the selection voltage matrices constituting the selection voltage matrices are composed substantially of .alpha..sub.1, .alpha..sub.2, . . . .alpha..sub.k, -.alpha..sub.1, -.alpha..sub.2, . . . , -.alpha..sub.k, and the number of the selection voltage vectors constituting the selection voltage rows is substantially 2K. Thus, the number of selection pulses necessary to select the row electrodes can be minimized, which is most effective for a fast response display.

The above description concerns a binary (two-valued) display. However, it is possible to realize a gradation display by using a similar method.

The order of an arrangement of the selection voltage vectors which constitute the selection voltage matrices is optional, and it is possible to replace the arrangement of the selection voltage vectors for each subgroup or a display information. In order to reduce the brightness nonuniformity of display in actual driving methods, it is sometimes preferred to conduct such replacement.

Hereinbelow, for simplifying explanation, there will be used a pattern wherein +V.sub.r as an element of the selection voltage vectors is expressed as "1" and -V.sub.r is expressed as "0", which is called "a selection pattern". Further, an arrangement of several selection patterns in a time sequential form is called "a selection code".

Now, explanation is made as to use of selection voltage matrix (a selection code) suitable for driving fast response LCDs.

As a result of practically using several kinds of selection voltage matrices, it has been found it preferable in a view of reducing the brightness nonuniformity of display in liquid crystal display elements to carry out in such a manner that the number of selection voltage vectors in the selection voltage matrices is 2I (I is a natural number of 2I.gtoreq.2K), and the matrices consist of an I number of selection voltage vectors which form a former half portion and an I number of selection voltage vectors which form the later half portion wherein the former half and the latter half are the same in absolute value and opposite in positive and negative signs. Although the reason why the above-mentioned arrangement of vectors can reduce the brightness nonuniformity of display in driving the liquid display elements is not clear, it can be considered that a waveform of voltage resulted between electrodes in effecting a display exhibits a form of alternating voltage having a uniform frequency spectrum regardless of a display information. Hereinbelow, a selection code having such arrangement of the selection voltage vectors is called in particular "an inversion code".

Specifically describing, when a selection code consists of a 2I number of selection patterns, and there is considered two groups: a first group of the first - I th selection patterns and a second group of the (I+1)th - 2Ith selection patterns, a selection code wherein the content of the s th selection pattern and the content of the (s+I)th selection pattern are in a negative relation should be used. Namely, a row electrode selection code should be formed so as to satisfy the relation as shown in List 3 when the s th selection pattern is expressed as W.sub.s. ##EQU1##

It was found for the inversion code to select rows of vectors having the order of [.alpha..sub.1, .alpha..sub.2, . . . .alpha..sub.k, -.alpha..sub.1, -.alpha..sub.2, . . . , -.alpha..sub.k ] in order to reduce the brightness nonuniformity of display when the selection voltage matrices are formed of a 2K number of selection voltage vectors.

Table 1 shows an example of selection code for row electrodes which is formed from a 4.times.4 Hadamard's matrix.

TABLE 1 ______________________________________ Selection pattern No. 1 2 3 4 5 6 7 8 ______________________________________ Row electrode 1 1 1 1 1 0 0 0 0 Row electrode 2 1 0 1 0 0 1 0 1 Row electrode 3 1 1 0 0 0 0 1 1 Row electrode 4 1 0 0 1 0 1 1 0 ______________________________________

The selection code of Table 1 satisfies that the selection voltage matrices have the order of [.alpha..sub.1, .alpha..sub.2, . . . .alpha..sub.k, -.alpha..sub.1, -.alpha..sub.2, . . . , -.alpha..sub.k ]. Further, selection codes shown in Tables 2 and 3 can be utilized in a case that a selection voltages (a selection pattern or patterns) are replaced for each subgroup. Numerical values in the Tables denote selection pattern number in Table 1. The selection patterns are applied to row electrodes time-sequentially from left to right. Table 2 shows that the selection patterns are changed after each row electrode subgroup has been selected. Table 3 shows that selection patterns are changed after every two row electrode subgroups are selected.

TABLE 2 ______________________________________ Subgroup No. 1 1 2 3 4 5 6 7 8 Subgroup No. 2 2 3 4 5 6 7 8 1 Subgroup No. 3 3 4 5 6 7 8 1 2 Subgroup No. 4 4 5 6 7 8 1 2 3 Subgroup No. 5 5 6 7 8 1 2 3 4 . . . . . . . . . . . . . . . . . . . .