,,CTEVH ,,3F];E

          ,,M>* #12-15, #2009

     ,,SAN ,,FRANCISCO1 ,,CALI=NIA



                 ,,NUBS
     ,,NEME? ,,UNI=M ,,BRL ,,SY/EM


            ,XS IMPLIC,NS 6!
              ,,SCI5TIFIC
           TRANSCRIB] & R1D]





            ,,PRES5T$ ,,BY3
             ,,JOYCE ,,HULL


              ,,9TRODUC;N            A#A

  ,! F/ "P ( ? TWO-"P "W%OP COV]$ !
IMPACT ( ? NEW BRL SY/EM ON ! LIT]>Y
TRANSCRIB] & R1D]4 ,T SES.N 9CLUD$ "S
4CUS.N AB ! PHILOSOPHY & R,NALE =
DEVELOP+ A NEW BRL CODE OR SY/EM4 ,!
H&-\ = T SES.N AL EXPLA9$ "O (! CRITICAL
3CEPTS ( ,,NUBS--T (! TWO MODES--
N>RATIVE & NOT,NAL4 ,AN "U/&+ ( T ASPECT
(! NEW CODE IS VITAL4 ,IF Y 7 N A#
6ATT5D T SES.N1 Y >E WELCOME 6ASK =A
COPY ( T H&\T4 ,X GIVES A FAIRLY
-PREH5SIVE >GU;T =! DEVELOP;T (A NEW BRL
CODE & ,DR4 ,NEME?'S APPROA* 6! TASK4
  ,! ,NEME? ,BRL ,CODE = ,MA!MATICS &
,SCI;E ,NOT,N1 #1972 ,V].N1 IS US$ =!
BRL V].N ( ? "W%OP4 ,X IS AL US$ 9 !
SIMBRL EXAMPLES1 = REPRES5T+ ! 8CURR5T
CODE0 =M (! EXAMPLES4




                                      #B
  ,! TOPICS A4RESS$ 9 ? "W%OP        B#A
9CLUDE3

,MA!MATICAL ,OP]ATORS
,FRAC;NS
  ,V]TICAL
  ,MIX$
  ,QUASI-,V]TICAL
  ,-PLEX
  ,SPATIAL
  ,SPATIAL ,-PLEX
  ,USE (! ,SLA%
,SUP]SCRIPTS & ,SUBSCRIPTS
  ,NUM]IC
  ,SIMPLE
  ,MULTILEVEL
  ,SIMULTANE\S & ,NON-SIMULTANE\S
,C.ELL,N & ,RENAM+ ,DIGITS 9 ,SUBTRAC;N
,RADICALS
  ,SIMPLE
  ,NE/$
  ,9DEX$
  ,4PLAY$
,CALCULATOR & ,-PUT] ,BRL
                                      #C
    ,,MA!MATICAL ,,OP]ATORS           #B
  ,MO/ (! OP]ATORS T H BE5 US$ 9 !
CURR5T ,NEME? CODE >E RETA9$4 ,NOTE T !
MULTIPLIC,N SIGNS >E NEW4

  ,PLUS  +  (346)
  ,M9US  -  (36)
  ,MULTIPLY
     CROSS  .[  (46, 246)
     DOT  ,]  (6, 12456)
     A/]ISK  _[  (456, 246)
  ,DIVIDE  ./  (46, 34)
  ,EQUAL SIGN  =  (123456)

  ,S ;A PLUS ;B DIVID$ BY ;C EQUALS ;D
WD 2 ;A+B./C = D

  ,NOTE T ? EXPRES.N IS PREC$$ BY
; (56), S9CE X IS EMB$D$4 ,? PLACES U 9
! NOT,NAL MODE4 ,IF ! EXPRES.N 7 4PLAY$1
T CELL WD 2 OMITT$ S9CE ALL 4PLAY$
EXPRES.NS >E REG>D$ Z NOT,NAL4

    DISTANCE = RATE.[TIME
                                      #D
  ,NOTE T 3TRAC;NS >E N P]MITT$ :5   A#B
9 ! NOT,NAL MODE4 ,? IS A BROAD]
RE/RIC;N ?AN T DEF9$ 9 ! CURR5T ,NEME?
CODE4

    ,,FRAC;NS
  ,! BASIC FRAC;N /RUCTURE IS RETA9$4

,V]TICAL FRAC;NS3 (F\R EXAMPLES)

  ?1/3#

  ?A/B#

  ?A+B/C#

  A+?B/C#+D

    ,MIX$ FRAC;NS (TWO EXAMPLES)

  #3?1/2#  ,FRAC;N HAS A HORIZONTAL B>4

  #3_?1_/2_#  ,! FRAC;N "P ( ? EXPRES;N
    IS L9E>--! #1 & #2 >E AT ! SAME
    LEVEL & >E SEP>AT$ 0A SLA%4       #E
,QUASI-V]TICAL FRAC;NS                #C

    ?A+B/C+D# & #3?X/Y#

  ,L9E> FRAC;N3 (,NUM]ATOR & DENOM9ATOR
    >E AT ! SAME LEVEL 9 PR9T4)

    A+B_/C+D   ,? IS  ;A+(B_/C)+D

    & %D N 2 9T]PRET$ Z  ;(A+B)_/(C+D)

,-PLEX FRAC;NS
  ,NOTE ! USE ( DOT #6 Z ! LEVEL (
  -PLEX;Y 9DICATOR4

   ,??A/B#,/?C/D#,#

,SPATIAL FRAC;NS4

           DISTANCE     ;D
   RATE = ?33333333# = ?33#
           TIME         T

  ,NOTE T ! DENOM9ATOR IS LEFT-ADJU/$1 N
  C5T]$4                              #F
                                     A#C
    ;D     #1     A+B
   ?33#   ?33#   ?333#
    DX     ;C     N

  ,AL NOTE T1 9 A SPATIAL FRAC;N1 :5"E !
NUM]ATOR OR ! DENOM9ATOR 3SI/S (A S+LE
DIGIT1 A NUM]IC 9DICATOR IS REQUIR$ 2F T
DIGIT4 ,IF ! NUM]ATOR OR DENOM9ATOR
3SI/S (A S+LE LR1 9 ! RANGE ;A "? ;J, !
LR SIGN ; (56) IS REQUIR$4
--------------------------------------#D

  ,SPATIAL -PLEX FRAC;N

    ,?1?1/4#,/1?3/5#,#
   ?333333333333333333#
    #5

  ,NOTE AG T ! DENOM9ATOR IS AG ALIGN$
6! LEFT1 N C5T]$4



                                      #G
                                     A#D
  ,! USE (! SLA% _/ (456*34) 9
MA!MATICS3

  ,9 A L9E> FRAC;N3  #1_/3

  ,Z DIVID]S 2T "PS (A DATE3  #6_/28_/95

    ,,SUP]SCRIPTS ,,& ,,SUBSCRIPTS

  ,! =MAT = SUP]SCRIPTS & SUBSCRIPTS HAS
N BE5 *ANG$4 ,? 9CLUDES ! SPECIAL TR1T;T
= SIMPLE SUBSCRIPTS L ;X1 & ;Y2_4

  X1+X2  (;X SUB #1 PLUS ;X SUB #2)

  ,NOTE3 ,NO SUBSCRIPT OR BASEL9E
9DICATORS >E REQUIR$ "H4

  A11X1+A12X2+ ,,' +A;1N"X;N = B1

  ,NOTE ! NEW ELLIPSIS &! NEW EQUAL
SIGN4

                                      #H
  ,VITAM9 ,B#12                      B#D

   (,THE #12 IS N A SUBSCRIPT1 S A NUMB]
SIGN IS REQUIR$ 2F T NUMB]4)

  ,SIMULTANE\S SUBSCRIPTS_/SUP]SCRIPTS

  P;A^.A^;X"+P;B^.B^;Y

--------------------------------------#E
    ,NON-SIMULTANE\S ,9DICES

  X^?F/G#";,L

  X;,L"^?F/G#

  ,9 ! F/ EXAMPLE1 ! SUP]SCRIPT IS CLOS]
TO ;X ?AN ! SUBSCRIPT2 9 ! SECOND
EXAMPLE1 ! SUBSCRIPT IS CLOS] TO ;X ?AN
! SUP]SCRIPT4 ,! BASE-LEVEL 9DICATOR 2T
! TWO 9DICES TELLS ! R1D] T !Y >E N
SIMULTANE\S4 ,! ORD] 9 : ! R1D] 5C.T]S !
9DICES TELLS HM : -ES F/ & : -ES SECOND4

                                      #I
                                     A#E
    ,,C.ELL,N ,,& ,,RENAM+ ,,DIGITS ,,9
    ,,SUBTRAC;N

  ,(T5 WE 5C.T] A PRO#M 9 SUBTRAC;N1 :5
A DIGIT 6BE SUBTRACT$ IS L>G] T ! DIGIT
ABV X4 ,= EXAMPLE3

     875
    -296
   333333

  ,9 DESCRIB+ ! CORRECT PROC$URE = ?
PRO#M1 A TEXTBOOK W (T5 %[ 8RE"ND0
NUMB]S ABV ! NUMB]S !Y REPLACE4 ,=
EXAMPLE1 ! NUMB] #15 W 2 PLAC$ ABV ! #5
&! #7 W 2 *ANG$ 6A #6_4 ,!N ! #6 IS
REPLAC$ 0! NUMB] #16 &! #8 IS REPLAC$ )A
#7_4 ,! PRO#M N[ LOOKS L ? 9 PR9T3

      ,',! *>T ON ! NEXT PAGE %[S H[ !
    ACTUAL SUBTRAC;N PRO#M N[ APPE>S 9
    PR9T4,'

                                     #AJ
                                     B#E

  ,TOP L9E F9AL RENAM+       #7 #16 #15
  ,F/ RENAM+ (6 IS C.ELL$)       #6 #15
  ,M9U5D (ALL >E C.ELL$)     #8  #7  #5
  ,M9US SIGN & SUBTRAH5D    -#2  #9  #6
  ,SEP>,N L9E """""""""""  3333333333333
  ,DI6];E """""""""""""""    #5  #7  #9

    ,! TOP TWO L9ES >E 9 A SMALL] FONT S
    T ALL (! COLUMNS C 2 ALIGN$ =
    -PUT,N4,'

  ,9 PR9T ? PRES5TS NO PRO#M 9 ALIGN;T
S9CE ! 8RE"ND NUMB]S0 C 2 WRITT5 9 A
SMALL FONT S Z N 64TURB ! ALIGN;T PRO#M4
,9 ! CURR5T BRL CODE1 H["E1 ? CR1TES A
DI6ICULTY 9 T ! #8, #7, & #5 M/ ALL 2
C.ELL$ & !N REPLAC$ ABV ) #2-CELL RENAM+
NUMB]S4 ,? WR1KS HAVOC ) ALIGN;T4 ,,NUBS
HAS A CL"E SUB/ITUTE = ? PROCESS4



                                     #AA
                                      #F
  ,=TUNATELY1 A TWO-DIGIT REPLACE;T
NUMB] 9 A SUBTRAC;N S*EME IS ALW 9 !
RANGE ( #10 TO #18 9CLUSIVE4 ,"!=E WE >E
A# 63TRIVE A 8TRICK0 = 5T]+ ? TWO-DIGIT
NUMB] 96"O CELL4 ,WE 5T] ? NUMB] Z A
DROPP$ NUMB]1 Z USUAL4 ,WE N[ ADD DOT #1
96! SAME CELL 69DICATE T ? IS A TWO-
DIGIT NUMB] ^: T5'S PLACE IS #1_4 ,?US !
NUMB]S F #10 TO #18 WD 2 REPRES5T$ 9 "O
CELL Z FOLL[S4

    Z   B   L   H   \   <   R   (   V

   #10 #11 #12 #13 #14 #15 #16 #17 #18

  ,9 ? SUBTRAC;N S*EME1 SUBTRAC;N IS
IMMLY POSSI# 9 E COLUMN4 ,"!=E1 "! >E NO
C.ELL$ DIGITS & REPLACE;T NUMB]S USE "O
CELL4
  ,! PRO#M DESCRIB$ ABV WD 2 BRLD Z3



                                     #AB
                                     A#F
  ,CURR5T CODE3      ,,NUBS3

     7  16  15         7R<
       [ 6] 15          6<
    [8][ 7][ 5]        875
   - 2   9   6        -296
   33333333333333    333333
     5   7   9         579

  ,SEE H[ CL1N ? IS4 ,"! IS NO NE$ = ANY
C.ELL,N 9DICATORS &! ALIGN;T IS MA9TA9$4
,9 ANY SUBTRAC;N PRO#M1 3SI/+ (A M9U5D
&A SUBTRAH5D1 ANY L9E ABV ! M9U5D WD 2
REG>D$ Z 8RE"ND0 NUMB]S4

    ,,C.ELL,N ,,9 ,,G5]AL
  ,SUBTRAC;N S*EMES D N H A MONOPOLY ON
! USE ( C.ELL,N4 ,9 >I?METIC1 C.ELL,N IS
US$ 9 ! PROCESS ( REDUC+ FRAC;NS 6L[E/
T]MS1 & 9 ! MULTIPLIC,N OR DIVI.N (
FRAC;NS4 ,9 ALGEBRA1 C.ELL,N IS US$ =
--------------------------------------#G
! SAME R1SONS4 ,H["E1 "! WE WD 2 D1L+ )
NUMB]-&-LR -B9,NS R ?AN J ) NUMB]S   #AC
Z 9 >I?METIC4                        A#G

   2G9 C.ELL,N  &  (12346)
   5D C.ELL,N   [  (246)

  ,IF ! TEXT 6BE C.ELL$ O3UPIES "O CELL1
! 5D-C.ELL,N 9DICATOR M/ 2 PLAC$ ABV OR
2L X1 Z APPROPRIATE4

       #1    #1
        _     _
       #3    #4     #1
      ?33#.[?33# = ?33#
       #8    #9     #6
        _     _
       #2    #3

  ,IF ! TEXT 6BE C.ELL$ O3UPIES M ?AN "O
CELL1 ! 2G9-C.ELL,N 9DICATOR &! 5D-
C.ELL,N 9DICATOR M/ 2 PLAC$ AT ! F/ &!
LA/ CELL1 RESPECTIVELY1 (! TEXT 6BE
C.ELL$4 ,^! 9DICATORS %D 2 PLAC$ ABV OR
2L ! TEXT 6BE C.ELL$1 Z APPROPRIATE4
  ,9 ! EXAMPLE %[N ON ! NEXT PAGE1 "! >E
F\R T]MS1 6! LEFT (! EQUAL SIGN1     #AD
EA* 9 P>5!SES4 ,! ?IRD "O IS         B#G
C.ELL$4

                &    [
    (X-A1)(X-A2)(X-A3)(X-A4) = 0
--------------------------------------#H
    ,,RADICALS
  ,! 2G9 RADICAL 9DICATOR IS ! SAME1 B !
RADICAL T]M9ATOR IS NEW3 [ (246)
  ,S1 ! SQU>E ROOT ( A+B IS3 ;>A+B[
,&! QUADRATIC =MULA WD 2

    X = ?-B_+>B^2"-4AC[/2A#

  ,NOTICE ! NEW SYMBOL =! PLUS-M9US
SIGN3 _+ (#456, #346)_4 ,NE/$ RADICALS
>E A BIT DI6]5T AL4 ,! LEVEL ( NE/+1 OR
-PLEX;Y 9DICATOR1 IS N[ 9DICAT$ AT !
2G9N+ (! EXPRES.N Z IS D"O ) -PLEX
FRAC;NS4
    ,S ! EXPRES.N

      ,>X+>X+Y[+>Y[,[

    IS A LEVEL-"O RADICAL4           #AE
                                     A#H
    ,,9DEX$ ,,RADICALS
  ,! =MAT = 9DICAT+ AN 9DEX =A RADICAL
IS NEW4 ,! 9DEX IS TR1T$ Z AN EXPON5T ON
! RADICAL SIGN1 & REQUIRES ! BASEL9E
9DICATOR 2F ! RADIC& IS 5T]$4

  ,! CUBE ROOT ( #2

    >^3"2[

  #3 "TS ! CUBE ROOT ( (;X PLUS ;Y)

    #3>^3"X+Y[

  ,! N? ROOT ( ;A

    >^N"A[

  ,! (;M PLUS N?) ROOT ( (;P PLUS ;Q)

    >^M+N"P+Q[


                                     #AF
                                      #I
  ,NE/$ ,9DEX$ ,RADICALS

    ,>^3">X^2"[,[ = ,>>^3"X^2"[,[

    ,>^3"X^2"+>^3"X^2"+Y^2"[+Y^2",[

  ,NE/$ RADICALS1 C 2 4PLAY$ SPATI,Y4

    ;333333333
    _  ;333 ;3
    >X+>X+Y+>Y

    ,,CALCULATOR ,,& ,,-PUT] ,,BRL
  ,,NUBS PROVIDES A ME?OD = %[+ A SEQU;E
( CALCULATOR KEY/ROKES :5 S* A SEQU;E IS
PRES5T 9 PR9T4 ,A KEY/ROKE IS ! PICTURE
(A KEYTOP ) XS LEG5D & IS 9TRODUC$ 9
,,NUBS 0! BRL "*  [  (246)_4 ,9 O!R
NOT,NAL 3TEXTS1 ? "* IS EI ! T]M9,N
9DICATOR OR ! 5D-C.ELL,N 9DICATOR4 ,:5 X
IS ! F/ "* (A KEY/ROKE 9 ! NOT,NAL MODE1
X _C 2 9T]PRET$ Z A T]M9,N 9DICATOR OR !
3TRAC;N = 8OW40 ,NEI C X 2 9T]PRET$ Z AN
5D-C.ELL,N 9DICATOR : IS ALW PLAC$   #AG
EI ABV OR 2L ! NOT,N 6BE C.ELL$4     A#I
,"!=E1 US+ ? SYMBOL 69TRODUCE A KEY/ROKE
IS UNAMBIGU\S4

  ,AF ? 2G9-KEYTOP-LEG5D 9DICATOR1 WE
WRITE ! KEYTOP LEG5D US+ /&>D ,,NUBS
NOT,N4 ,A SPACE FOLL[S ! KEYTOP LEG5D 2F
BRAILL+ ! NEXT KEY/ROKE4 ,KEY/ROKES >E
NOT,NAL & SPATIAL & M/ 2 TR1T$ ACLY4
-------------------------------------#AJ
  ,,EXAMPLES (%[+ KEY/ROKES)

#1] ,PRESS ;[+_/-]

  6*ANGE ! SIGN (! NUMB]4 (,! LEG5D ON !
KEYTOP IS PLUS-SLA%-M9US4)

  ,? S]IES ( CALCULATOR KEY SYMBOLS

  #2.41$K,,EE]0$K./]7.4$K,,EE]21$K.K]

  WD N[ 2 BRLD Z3

  #2]41 [,,EE #0 [./ #7]4 [,,EE #21 [=
                                     #AH
   (,? IS A SEQU;E ( KEY/ROKES 9    A#AJ
: "S >E NUMB]S & "S >E NOT4)

  ,T'S ALL = TD4 ,DR4 ,NEME? HAS WRITT5
RULES = _M O!R ASPECTS (! SCI5TIFIC
SPECTRUM T WE D N H "T 6G 96IN ? SES.N4
,HE HAS DEF9$ ! H&L+ ( FUNC;NS1
MATRICES1 DET]M9ANTS1 SY/EMS ( EQU,NS1
OV]SCRIPTS & "USCRIPTS1 & HAS DEF9$ BRL
REPRES5T,NS = _M SYMBOLS & GEOMETRIC
%APES1 BO? 9 BRL & Z TACTILE GRAPHICS4
,8 FULL DRAFT DOCU;T1 : IS N[ -PLETE1
REQUIRES AB #170 PR9T PAGES4
  ,I WD APPRECIATE X V M* IF Y WD %>E )
ME ANY ]RORS Y F9D OR SU7ES;NS Y H T WD
IMPROVE ? PRES5T,N4 ,IF Y >E 9T]E/$ 9 M
DETAILS1 PL1SE 3TACT ME AT3

    ,JOYCE ,HULL #407-349-5059
    _+JHULL@FBS.NET_:

  ,9 ,,NUBS1 MY ;E-MAIL A4RESS WD BE3
;JHULL@AFBS]NET] ,WE WD NO L;G] NE$ !
,-PUT] ,BRL ,CODE IF ,,NUBS IS ADOPT$4
                                     #AI