`
`
`
`Europaisches Patentamt
`European Patent Office
`Office europeen des brevets
`
`© Publication number:
`
`0 6 8 0 2 2 3 A 1
`
`EUROPEAN PATENT A P P L I C A T I O N
`
`© Application number: 94302888.6
`
`int. Ci.6; H04N 9/64, H04N 9/67
`
`@ Date of filing: 22.04.94
`
`@ Date of publication of application:
`02.11.95 Bulletin 95/44
`
`© Designated Contracting States:
`AT BE CH DE DK ES FR GB GR IE IT LI LU MC
`NL PT SE
`
`© Applicant: WINBOND ELECTRONICS
`CORPORATION
`No. 4, Yen-Hsin-San Road,
`Science-Based Industrial Park
`Hsinchu City (TW)
`
`@ Inventor: Shyu, Rong-Fuh
`No. 4, Yen-Hsin-San Rd., Science-Based Ind.
`Park
`Hsinchu City (TW)
`
`© Representative: Barlow, Roy James
`J.A. KEMP & CO.
`14, South Square
`Gray's Inn
`London WC1R 5LX (GB)
`
`© Method and apparatus for color space conversion.
`
`© A method and apparatus for performing color space conversion between digitized YCbCr components and
`digitized RGB components uses a color lookup table unit (1,1 A) which is provided with transformation
`component values based on a selected one of two sets of conversions. A plurality of adder units are coupled to
`the lookup table unit (1,1 A) so as to receive the outputs thereof and generate individual color components of
`converted space by adding the transformation component values corresponding to each of the individual color
`components of converted space relative to the color components of original space.
`1A
`
`22A
`FIRST
`COMPLEMENT MEANS
`
`Cb-
`
`23A
`
`I SECOND I COMPLEMENT I
`I
`MEANS
`
`Cr-
`
`CO
`CM
`CM
`
`00
`CO
`
`[~102A
`12A
`TABLE
`INPUT MEANS
`C32 I Cb-128
`31A
`1 P2,A>
`SECOND POLARITY I
`FIRST POLARITY
`CONTROL MEANS
`[control MEANS j
`'
`13A
`HA
`s
`!
`TABLE
`TABLE
`I
`C23 j Cr-128 | ,
`C13|Cr-12S|
`~H &a ;
`FOURTH POLARITY!
`CONTROL MEANS I
`
`11A
`TABLE
`C22|Cb-128
`
`103A
`JlNPUT
`Imeans
`33AA
`THIRD POLARITY
`CONTROL MEANS
`
`1 3 5
`FIRST |,
`
`/a3A
`
`44Al
`/
`I 1 1 FOURTH
`/ I ADDER
`
`A2A
`second!)
`ADDER 1 '
`
`71
`LIMIT CKt|j
`
`LIMIT CKTjj
`
`LIMIT CKTj^
`
`FIG. A
`
`Rank Xerox (UK) Business Services
`(3. 10/3.09/3.3.4)
`
`Unified Patents, LLC v. Elects. & Telecomm. Res. Inst., et al.
`
`Ex. 1032, p. 1
`
`
`
`EP 0 680 223 A1
`
`2
`
`35
`
`45
`
`5
`
`io
`
`20
`
`25
`
`This invention relates to a method and apparatus for performing color space conversion, more
`particularly to a method and apparatus for performing color space conversion between digitized YCbCr
`color components and digitized RGB color components.
`Nowadays, due to the growing popularity of multimedia applications, the development of advanced data
`processing techniques for digital audio data and digital video data has become more and more important. It
`is noted that, due to the limited bandwidth of the transmission networks and the limited storage spaces of
`the existing computer systems, digital video data have to be compressed before transmission or storage.
`Thereafter, the compressed data are decompressed so as to obtain the original digital video data from the
`storage or transmission media.
`Presently, digitized YCbCr components, wherein the Y component represents luminance or picture
`brightness, the Cb component (B-Y) represents the scaled difference between the blue value (B) and the
`luminance (Y), and the Cr component (R-Y) represents the scaled difference between the red value (R) and
`the luminance (Y), are used in known compression algorithms since the digitized YCbCr components
`occupy less bandwidth when compared to digitized RGB (Red-Green-Blue) components which are obtained
`75 by passing analog RGB signals through an analog-to-digital converting means. However, the existing
`imaging and displaying apparatuses generally use analog RGB signals to represent image. Therefore, the
`analog RGB signals must initially pass through an analog-to-digital converting means and are then
`converted into digitized YCbCr components before compression. The digitized YCbCr components are
`converted into the digitized RGB components after decompression. If necessary, the digitized RGB
`components are converted into analog RGB signals.
`Although there are many conventional techniques for color space conversion, the architecture of the
`conventional techniques permits conversion in only one mode, that is, either converting YCbCr components
`to RGB components or converting RGB components to YCbCr components. Additionally, the conventional
`techniques are expensive due to the large memory requirements thereof. Furthermore, the conventional
`techniques that use multipliers are relatively expensive and have a relatively slow operating speed.
`Therefore, the main object of the present invention is to provide a method and apparatus for performing
`color space conversion between digitized YCbCr color components and digitised RGB color components,
`which method and apparatus are inexpensive and are highly efficient.
`Accordingly, an apparatus of the present invention is capable of performing color space conversion
`30 between digitized YCbCr color components and digitized RGB color components. When converting the
`digitized YCbCr color components to the digitized RGB color components, digitized transformation compo-
`nent values corresponding to a Y-in-R component, a Cb-in-R component, a Cr-in-R component, a Y-in-G
`component, a Cb-in-G component, a Cr-in-G component, a Y-in-B component, a Cb-in-B component and a
`Cr-in-B component, are placed into a programmable color lookup table means based on a set of
`conversions from individual digitized Y, Cb and Cr components. The color lookup table means has a
`plurality of address inputs and includes first to ninth segments. The transformation component values
`corresponding to the Y-in-R component, the Y-in-G component, the Y-in-B component, the Cb-in-R
`component, the Cb-in-G component, the Cb-in-B component, the Cr-in-R component, the Cr-in-G compo-
`nent and the Cr-in-B component occupy the first to ninth segments, respectively. The digitized Y, Cb and
`40 Cr components are inputted to the address inputs of the color lookup table means to effect reference to the
`corresponding Y-in-R transformation component value, the corresponding Cb-in-R transformation compo-
`nent value, the corresponding Cr-in-R transformation component value, the corresponding Y-in-G trans-
`formation component value, the corresponding Cb-in-G transformation component value, the corresponding
`Cr-in-G transformation component value, the corresponding Y-in-B transformation component value, the
`corresponding Cb-in-B transformation component value and the corresponding Cr-in-B transformation
`component value. The corresponding Y-in-R transformation component value, the corresponding Cb-in-R
`transformation component value and the corresponding Cr-in-R transformation component value are added
`to obtain the digitized R component. The corresponding Y-in-G transformation component value, the
`corresponding Cb-in-G transformation component value and the corresponding Cr-in-G transformation
`component value are added to obtain the digitized G component. Finally, the corresponding Y-in-B
`transformation component value, the corresponding Cb-in-B transformation component value and the
`corresponding Cr-in-B transformation component value are added to obtain the digitized B component.
`When converting the digitized RGB color components to the digitized YCbCr color components,
`digitized transformation component values corresponding to an R-in-Y component, a G-in-Y component, a
`55 B-in-Y component, an R-in-Cb component, a G-in-Cb component, a B-in-Cb component, an R-in-Cr
`component, a G-in-Cr component and a B-in-Cr component, are placed into the programmable color lookup
`table means based on a set of conversions from individual digitized R, G and B components. The
`transformation component values corresponding to the R-in-Y component, the R-in-Cb component, the R-in-
`
`50
`
`Unified Patents, LLC v. Elects. & Telecomm. Res. Inst., et al.
`
`Ex. 1032, p. 2
`
`
`
`EP 0 680 223 A1
`
`5
`
`io
`
`is
`
`Cr component, the G-in-Y component, the G-in-Cb component, the G-in-Cr component, the B-in-Y compo-
`nent, the B-in-Cb component and the B-in-Cr component occupy the first to ninth segments of the color
`lookup table means, respectively. The digitized R, G and B components are inputted to the address inputs
`of the color lookup table means to effect reference to the corresponding R-in-Y transformation component
`value, the corresponding G-in-Y transformation component value, the corresponding B-in-Y transformation
`component value, the corresponding R-in-Cb transformation component value, the corresponding G-in-Cb
`transformation component value, the corresponding B-in-Cb transformation component value, the cor-
`responding R-in-Cr transformation component value, the corresponding G-in-Cr transformation component
`value and the corresponding B-in-Cr transformation component value. The corresponding R-in-Y transforma-
`tion component value, the corresponding G-in-Y transformation component value and the corresponding B-
`in-Y transformation component value are added to obtain the digitized Y component. The corresponding R-
`in-Cb transformation component value, the corresponding G-in-Cb transformation component value and the
`corresponding B-in-Cb transformation component value are added to obtain the digitized Cb component.
`The corresponding R-in-Cr transformation component value, the corresponding G-in-Cr transformation
`component value and the corresponding B-in-Cr transformation component value are added to obtain the
`digitized Cr component.
`In another aspect of the present invention, a method for converting digitized YCbCr color components
`to digitized RGB color components includes the steps of: providing a color lookup table means which has a
`plurality of address inputs and which includes a first segment provided with a digitized transformation
`component value corresponding to a Cb-in-G component, a second segment provided with a digitized
`transformation component value corresponding to a Cb-in-B component, a third segment provided with a
`digitized transformation component value corresponding to a Cr-in-R component, and a fourth segment
`provided with a digitized transformation component value corresponding to a Cr-in-G component; inputting
`the digitized Y, Cb and Cr components to the address inputs of the color lookup table means to effect
`reference to the corresponding Cb-in-G transformation component value, the corresponding Cb-in-B
`transformation component value, the corresponding Cr-in-R transformation component value and the
`corresponding Cr-in-G transformation component value; adding the Y component and the corresponding Cr-
`in-R transformation component value to obtain the digitized R component; adding the Y component, the
`corresponding Cb-in-G transformation component value and the corresponding Cr-in-G transformation
`component value to obtain the digitized G component; and adding the Y component and the corresponding
`Cb-in-B transformation component value to obtain the digitized B component.
`Other features and advantages of the present invention will become apparent in the following detailed
`description of the preferred embodiments, with reference to the accompanying drawings, of which:
`Figs. 1A, 1B and 1C are schematic block diagrams showing an apparatus for performing color space
`conversion between digitized YCbCr color components and digitized RGB color components in accor-
`dance with a first embodiment of the present invention;
`Fig. 2 is a schematic block diagram showing a first complement means and an address decoder of the
`apparatus of Fig. 1 ;
`Fig. 3 is a schematic block diagram illustrating one of the polarity control means shown in Fig. 1;
`Fig. 4 is a schematic block diagram of an apparatus for converting digitized YCbCr components to
`digitized RGB components in accordance with a second embodiment of the present invention;
`Fig. 5 is a schematic block diagram showing how a programmable color lookup table means of the
`apparatus shown in Fig. 1 is programmed;
`Fig. 6 is a table illustrating an address decoding method employed in the present invention; and
`Fig. 7 illustrates the operation of a programming control circuit upon input of differing combinations of
`selecting signals, which programming control circuit is used to program the programmable color lookup
`table means of the apparatus shown in Fig. 1.
`In the present invention, each of the digitized Y, Cb and Cr components and each of the digitized R, G
`and B components is an 8-bit component. Direct conversion of digitized RGB components to digitized
`50 YCbCr components is achieved in the following manner:
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`55
`
`0 . 2 2 9
`Y
`Cb = - 0 . 1 7 3
`0 . 5 1 1
`cr
`
`0 . 5 8 7
`- 0 . 3 3 8
`- 0 . 4 2 8
`
`0 . 1 1 4
`0 . 5 1 1
`- 0 . 0 8 3
`
`1 2 8
`R-128
`G-128 + 1 2 8
`1 2 8
`B-128
`
`Direct conversion of digitized YCbCr components to RGB components is achieved in the following manner:
`
`3
`
`Unified Patents, LLC v. Elects. & Telecomm. Res. Inst., et al.
`
`Ex. 1032, p. 3
`
`
`
`EP 0 680 223 A1
`
`R
`G =
`B
`
`1 . 3 7 0
`1 - 0 . 0 0 1
`1 - 0 . 3 3 6 - 0 . 6 9 8
`0 . 0 0 1
`1
`1 . 7 3 3
`
`1 2 8
`Y -128
`Cb-128 + 1 2 8
`1 2 8
`C r - 1 2 8
`
`The above conversions (a) and (b) can be represented by the following equation:
`
`3
`C n m ( P I m - 1 2 8 ) +128, n = l , 2 , 3
`POn=Z
`m = l
`
`( c )
`
`5
`
`10
`
`75
`
`25
`
`30
`
`35
`
`40
`
`In the equation (c), Pirn is defined as a color component of an original space, POn is defined as a color
`component of a converted space, and Cnm is defined as a transformation coefficient corresponding to an
`nth color component of the converted space relative to an mth color component of the original space, and
`the product of Cnm and Plm-128 is defined as a transformation component value corresponding to a Plm-
`in-POn component. Therefore, in the present embodiment, when P01 , P02 and P03 represent Y, Cb and
`Cr components respectively, PI1, PI2 and PI3 represent R, G and B components respectively. Similarly,
`20 when P01, P02 and P03 represent R, G and B components respectively, PI1, PI2 and PI3 represent Y, Cb
`and Cr components respectively.
`Referring to Figs. 1A, 1B, 1C, 2 and 3, an apparatus for performing color space conversion between
`digitized YCbCr color components and digitized RGB color components in accordance with a first
`embodiment of the present invention includes a programmable color lookup table means 1, first to third
`complement means 21 to 23, first to ninth polarity control means 31 to 39, first to third adder means and
`first to third compensation and limit circuits 51 to 53.
`In the present embodiment, the programmable color lookup table means 1 is a RAM device. The lookup
`table means 1 has a plurality of address inputs and includes first to ninth segments 11 to 19, and input
`means 101, 102 and 103. The input means 101, 102 and 103 receive digitized PI1, PI2 and PI3 for
`addressing the address inputs of the lookup table means 1 . In the present embodiment, each of the input
`means 101,102,103 is an address decoder. When converting the RGB components to the YCbCr compo-
`nents, the digitized transformation component values corresponding to an R-in-Y component, an R-in-Cb
`component, an R-in-Cr component, a G-in-Y component, a G-in-Cb component, a G-in-Cr component, a B-
`in-Y component, a B-in-Cb component and a B-in-Cr component are programmed into the first to ninth
`segments 11 to 19, respectively, based on the conversion (a). As best shown in Figs. 5 and 7, the
`programming of the lookup table means 1 is accomplished by a programming control circuit 8 and a
`demultiplexer 9. The demultiplexer 9 is connected to the first, second and third complement means 21 to
`23. The programming control circuit 8 has a WRITE signal line and a DATA bus that are connected to the
`first to ninth segments 11 to 19 of the lookup table means 1. The control circuit 8 further has a SELECTOR
`signal line and a ADDRESS signal line that are connected to the demultiplexer 9. The control circuit
`provides a 2-bit selecting signal to the demultiplexer 9 via the SELECTOR signal line. When the selecting
`signal is 01, the first to third segments 11 to 13 are selected to be programmed. When the selecting signal
`is 10, the fourth to sixth segments 14 to 16 are selected to be programmed. When the selecting signal is
`11, the seventh to ninth segments 17 to 19 are selected to be programmed. When the selecting signal is
`45 00, programming of the lookup table means 1 is prohibited. Since the segments 11 to 19 of the lookup table
`means 1 corresponding to the same component of the original space are written thereinto simultaneously,
`programming of the entire lookup table means 1 requires only 3*128 = 384 write cycles. When converting
`the YCbCr components to the RGB components, the digitized transformation component values correspond-
`ing to a Y-in-R component, a Y-in-G component, a Y-in-B component, a Cb-in-R component, a Cb-in-G
`component, a Cb-in-B component, a Cr-in-R component, a Cr-in-G component and a Cr-in-B component are
`programmed into the first to ninth segments 11 to 19, respectively, based on the conversion (b) by a similar
`programming procedure as described above.
`It should be recognized that the conversion from digitized YCbCr components to digitized RGB
`components is similar to the conversion from digitized RGB components to digitized YCbCr components.
`55 Therefore, the following description of the first embodiment of the present invention is based on the
`conversion from digitized RGB components to digitized YCbCr components only.
`The first complement means 21 is connected to the input means 101 and receives the digitized R color
`component. The first complement means 21 generates 2's complement of the seven lower bits (Plm6 to
`
`50
`
`4
`
`Unified Patents, LLC v. Elects. & Telecomm. Res. Inst., et al.
`
`Ex. 1032, p. 4
`
`
`
`EP 0 680 223 A1
`
`5
`
`io
`
`is
`
`20
`
`25
`
`35
`
`PlmO) of the R color component when the most significant bit (Plm7) of the R color component is equal to
`0.
`
`The second complement means 22 is connected to the input means 102 and receives the digitized G
`color component. The second complement means 22 generates 2's complement of the seven lower bits of
`the G color component when the most significant bit of the G color component is equal to 0.
`The third complement means 23 is connected to the input means 103 and receives the digitized B color
`component. The third complement means 23 generates 2's complement of the seven lower bits of the B
`color component when the most significant bit of the B color component is equal to 0.
`The first polarity control means 31 includes a complement means 310 connected to an output of the
`first segment 1 1 of the lookup table means 1 , an output shading circuit 31 1 connected to the complement
`means 310 and a detector 312. The complement means 310 generates 2's complement of the output of the
`first segment 1 1 of the lookup table means 1 when the most significant bit (Plm7) of the digitized R color
`component is equal to 0. The detector 312 detects whether the value of the digitized R component is 128
`by means of an address signal (AmO) from the input means 101 and the most significant bit (Plm7) of the R
`component. The detector 312 generates a disabling signal when the value of the R component is 128. The
`shading circuit 311 outputs a value of 0 upon reception of the disabling signal from the detector 312.
`Otherwise, the shading circuit 311 outputs the output of the complement means 310.
`The structure of the second polarity control means 32 is similar to that of the first polarity control means
`31 . The complement means (not shown) of the control means 32 is connected to an output of the second
`segment 12 of the lookup table means 1. The output shading circuit (not shown) of the control means 32 is
`connected to the complement means. The complement means generates 2's complement of the output of
`the second segment 12 of the lookup table means 1 when the most significant bit of the digitized R color
`component is equal to 0. The detector (not shown) of the control means 32 detects whether the value of the
`digitized R component is 128 by means of the address signal from the input means 101 and the most
`significant bit of the R component. The detector of the control means 32 generates a disabling signal when
`the value of the R component is 128. The shading circuit of the control means 32 outputs a value of 0 upon
`reception of the disabling signal from the detector. Otherwise, the shading circuit outputs the output of the
`complement means.
`The structure of the third polarity control means 33 is similar to that of the first polarity control means
`30 31. The complement means (not shown) of the control means 33 is connected to an output of the third
`segment 13 of the lookup table means 1. The output shading circuit (not shown) is connected to the
`complement means. The complement means generates 2's complement of the output of the third segment
`13 of the lookup table means 1 when the most significant bit of the digitized R color component is equal to
`0. The detector (not shown) of the control means 33 detects whether the value of the digitized R component
`is 128 by means of the address signal from the input means 101 and the most significant bit of the R
`component. The detector generates a disabling signal when the value of the R component is 128. The
`shading circuit outputs a value of 0 upon reception of the disabling signal from the detector. Otherwise, the
`shading circuit outputs the output of the complement means.
`The structure of the fourth polarity control means 34 is similar to that of the first polarity control means
`40 31 . The complement means (not shown) of the control means 34 is connected to an output of the fourth
`segment 14 of the lookup table means 1. The output shading circuit (not shown) of the control means 34 is
`connected to the complement means. The complement means generates 2's complement of the output of
`the fourth segment 14 of the lookup table means 1 when the most significant bit of the digitized G color
`component is equal to 0. The detector (not shown) of the control means 34 detects whether the value of the
`45 digitized G component is 128 by means of an address signal from the input means 102 and the most
`significant bit of the G component. The detector generates a disabling signal when the value of the G
`component is 128. The shading circuit outputs a value of 0 upon reception of the disabling signal from the
`detector. Otherwise, the shading circuit outputs the output of the complement means.
`The structure of the fifth polarity control means 35 is similar to that of the first polarity control means
`50 31. The complement means (not shown) of the control means 35 is connected to an output of the fifth
`segment 15 of the lookup table means 1. The output shading circuit (not shown) of the control means 35 is
`connected to the complement means. The complement means generates 2's complement of the output of
`the fifth segment 15 of the lookup table means 1 when the most significant bit of the digitized G color
`component is equal to 0. The detector (not shown) of the control means 35 detects whether the value of the
`55 digitized G component is 128 by means of the address signal from the input means 102 and the most
`significant bit of the G component. The detector generates a disabling signal when the value of the G
`component is 128. The shading circuit outputs a value of 0 upon reception of the disabling signal from the
`control means 35. Otherwise, the shading circuit outputs the output of the complement means.
`
`5
`
`Unified Patents, LLC v. Elects. & Telecomm. Res. Inst., et al.
`
`Ex. 1032, p. 5
`
`
`
`EP 0 680 223 A1
`
`5
`
`is
`
`25
`
`35
`
`20
`
`The structure of the sixth polarity control means 36 is similar to that of the first polarity control means
`31. The complement means (not shown) of the control means 36 is connected to an output of the sixth
`segment 16 of the lookup table means 1. The output shading circuit (not shown) of the control means 36 is
`connected to the complement means. The complement means generates 2's complement of the output of
`the sixth segment 16 of the lookup table means 1 when the most significant bit of the digitized G color
`component is equal to 0. The detector (not shown) of the control means 36 detects whether the value of the
`digitized G component is 128 by means of the address signal from the input means 102 and the most
`significant bit of the G component. The detector generates a disabling signal when the value of the G
`component is 128. The shading circuit outputs a value of 0 upon reception of the disabling signal from the
`io detector. Otherwise, the shading circuit outputs the output of the complement means.
`The structure of the seventh polarity control means 37 is similar to that of the first polarity control
`means 31 . The complement means (not shown) of the control means 37 is connected to an output of the
`seventh segment 17 of the lookup table means 1. The output shading circuit (not shown) of the control
`means 37 is connected to the complement means. The complement means generates 2's complement of
`the output of the seventh segment 17 of the lookup table means 1 when the most significant bit of the
`digitized B color component is equal to 0. The detector (not shown) of the control means 37 detects
`whether the value of the digitized B component is 128 by means of an address signal from the input means
`103 and the most significant bit of the B component. The detector generates a disabling signal when the
`value of the B component is 128. The shading circuit outputs a value of 0 upon reception of the disabling
`signal from the detector. Otherwise, the shading circuit outputs the output of the complement means.
`The structure of the eighth polarity control means 38 is similar to that of the first polarity control means
`31 . The complement means (not shown) of the control means 38 is connected to an output of the eighth
`segment 18 of the lookup table means 1. The output shading circuit (not shown) of the control means 38 is
`connected to the complement means. The complement means generates 2's complement of the output of
`the eighth segment 18 of the lookup table means 1 when the most significant bit of the digitized B color
`component is equal to 0. The detector (not shown) of the control means 38 detects whether the value of the
`digitized B component is 128 by means of the address signal from the input means 103 and the most
`significant bit of the B component. The detector generates a disabling signal when the value of the B
`component is 128. The shading circuit outputs a value of 0 upon reception of the disabling signal from the
`30 detector. Otherwise, the shading circuit outputs the output of the complement means.
`The structure of the ninth polarity control means 39 is similar to that of the first polarity control means
`31. The complement means (not shown) of the control means 39 is connected to an output of the ninth
`segment 19 of the lookup table means 1. The output shading circuit (not shown) of the control means 39 is
`connected to the complement means. The complement means generates 2's complement of the output of
`the ninth segment 19 of the lookup table means 1 when the most significant bit of the digitized B color
`component is equal to 0. The detector (not shown) of the control means 39 detects whether the value of the
`digitized B component is 128 by means of the address signal from the input means 103 and the most
`significant bit of the B component. The detector generates a disabling signal when the value of the B
`component is 128. The shading circuit outputs a value of 0 upon reception of the disabling signal from the
`40 detector. Otherwise, the shading circuit outputs the output of the complement means.
`The first adder means includes a first adder 41 and a second adder 42. The first adder 41 is connected
`to the output shading circuit 311 of the first output polarity control means 31 and to the output shading
`circuit of the fourth output polarity control means 34 so as to generate an output corresponding to the sum
`of an output of the shading circuit 31 1 of the first output polarity control means 31 and an output of the
`shading circuit of the fourth output polarity control means 34. The second adder 42 is connected to the
`output shading circuit of the seventh