**Fun with the HP 71B II**

Four years ago, I had fun with the HP 71B programming:

That has been too long ago. Time to pull out the 71B again.

**Digital Root of an Integers**

Add all the numbers of an integer and repeat until you
have a single digit (1-9).

**Program DROOT (52 bytes)**

10 DESTROY N

20 INPUT “INTEGER:”;N

22 N=IP(N)

30 D=1+MOD(N-1,9)

40 DISP D

**Easy Traverse Calculation**

Calculates the new point knowing the original
coordinates, direction, and angle of travel. The angle 0° comes from due
east and rotates counterclockwise (see diagram below).

**Program TRAVEZ (216 bytes)**

15 DEGREES

20 INPUT “INIT. EASTING:”;E

25 INPUT “INIT. NORHTING:”;N

30 D=0

40 INPUT “DISTANCE:”;I

45 INPUT “ANGLE:”;A

50 E=I*COS(A)+E

55 N=I*SIN(A)+N

57 D=D+I

60 DISP N;’,’;E

65 PAUSE

70 INPUT “DONE? (Y=1,N=0)”;X

75 IF X=0 THEN 40

90 DISP “TOTAL DIST:”;D

**Integral Using Simpson’s Rule**

∫ FNF(X) dX from X = a to X = b

Line 10 is where you have to define your function
(of X).

**Program SIMPSON (200+ bytes)**

10 DEF
FNF(X)=insert function of X here

30
INPUT “LOWER:”;A

32
INPUT “UPPER:”;B

34
INPUT “# PART’NS (EVEN):”;N

36
RADIANS

38
T=FNF(A)+FNF(B)

40
H=(B-A)/N

50 FOR
I=1 TO N-1

52 IF
FP(I/2)=0 THEN 54 ELSE 56

54
T=2*FNF(A+I*H)+T @ GOTO 58

56
T=4*FNF(A+I*H)+T

58 NEXT
I

60
T=T*H/3

62 DISP
“INTEGRAL:”;T

**Expanding the Binomial (ax+b)^n**

BINOMEXP
gives the coefficients of the expansion of (ax+b)^n.

**Program BINOMEXP (about 189 bytes)**

10
DESTROY A,B,N,L,I,C

12
OPTION BASE 0

14 DISP
‘exapand(Ax+B)^N’ @ WAIT 1

16
INPUT “A,B,N”;A,B,N

18 DIM
L(N)

20 FOR
I=0 TO N

22
C=FACT(N)/(FACT(I)*FACT(N-I)) \\ FACT is
the factorial function

24
L(I)=C*A^(N-I)*B^I

26 DISP
“L(“; I; ”):”; L(I); “x^”; N-I @ PAUSE

28 NEXT
I

40 DISP
“DONE, CHECK L.”

**Synthetic Division**

Divide the polynomial p(x) by (x-R). P is the array of p(x), Q is the array
representing the quotient q(x), and E is the remainder. Hence:
P(x)/(x-R) = Q(x) + E/(x-R)

**Program SYNTH (304 bytes)**

10 DESTROY P,I,Q,R,E

12 OPTION BASE 0

14 DIPS “P(X)/(X-R)” @ WAIT 1

16 INPUT “DEGREE OF P(X):”;N

18 DIM P(N),Q(N)

20 FOR I=0 TO N

22 DISP “COEF OF x^”;N-1 @ PAUSE

24 INPUT P(I) @ P(I)=Q(I)

26 NEXT I

30 INPUT “R:’;R

40 FOR I=0 TO N-1

42 Q(I+1)=R*Q(I)+P(I+1)

44 NEXT I

50 E=Q(N)

60 DIM Q(N-1)

70 DISP “COEF OF Q(X)”

72 FOR I=0 TO N-1

74 DISP Q(I); “x^”; N-I-1 @ PAUSE

76 NEXT I

80 DISP “REMAIN:”; E; “/(x-“; R; “)”

**Dew Point Measurement (in °F)**

**Program DEWPOINT (159 bytes)**

10 DESTROY T,H,V,W,C,D

20 INPUT “TEMP °F”;T

22 C=(T-32)*5/9

26 INPUT “REL HUMIDITY (%):”;H

30 V=(LOG(H%1)+17.27*C/(237.3+C))/17.27

32 W=237.3*V/(1-V)

40 D=9/5*W+32

42 DISP “DEW POINT °F:”;D

// Degree symbol:
[ g ] [RUN] (CTRL) [ A ]