HP-45 Reference the 1973 successor to the HP-35 · gold shift · 66 entries

The HP-45: the HP-35’s functions plus everything a gold shift key could add: nine storage registers with arithmetic in them, LAST x, FIX and SCI, three angular modes, degrees-minutes-seconds, polar and rectangular conversion, mean and standard deviation, percentages, factorials and three unit constants. This sheet is the keyboard drawn from the handbook’s figure, a guide to the machine from the stack outward, an index of every key and function with its handbook page, and the handbook’s vector-sum example traced through the stack and the summation registers. The gold key is written as ■, the blank square it is.

■ the gold shift key · key a key · 0.00 the display
Source: HP-45 Owner’s Handbook, HP 00045-90300 Rev. 11/74 (Hewlett-Packard, Cupertino, 1974), with the HP-45 Quick Reference Guide; page numbers are the handbook’s printed pages.
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The Keyboard

35 keys · one gold shift · drawn to the proportions of the machine
-1.234567809-45
OFFON
yx1/x
logln
10xex
SCIFIX
  
√xx2
→R→P
SIN⁻¹SIN
COS⁻¹COS
TAN⁻¹TAN
n!x⇄y
x̄,sR↓
→D.MSSTO
D.MS→RCL
Δ%%
DEGENTER↑
RADCHS
GRDEEX
CLEARCLx
 −
cm/in7
kg/lb8
ltr/gal9
 +
 4
 5
 6
 ×
 1
 2
 3
 ÷
LAST x0
π.
Σ−Σ+
hpHEWLETT · PACKARD45

Thirty-five keys and a gold one

The HP-45 keyboard is the HP-35’s with a gold shift key in the top right corner: almost every key now does two jobs, the white one printed on the cap and the gold one printed on the case above it. Press gold, then the key. The handbook draws a shifted function in a box, and this sheet draws the gold key as the blank square it is.

plain
the legend on the cap
■ key
the gold legend above it
STO + n
register arithmetic: the operator between STO or RCL and the digit
y ENTER↑ x
every two-number function takes Y then X; the result of a pair comes back the same way

What the shift bought: a second logarithm base, FIX and SCI, x² alongside √x, the inverse trig functions, n!, mean and standard deviation, degrees-minutes-seconds both ways, Δ%, three angular modes, three unit constants, π, Σ− and LAST x.

The key colours group by use: black for functions, grey for control and arithmetic, light for the digits.

the gold shift key — blank on the machinea gold legend on the case: press gold firstblack: functions and %grey: control keys and operators

HP-45 Guide

the machine, and how to make it do things

Anatomy four things worth seeing laid out

The same four registers, plus one behind them

The HP-45’s X, Y, Z and T work exactly as the HP-35’s: ENTER↑ lifts, an operator drops, and a dropping stack copies T into Z. The HP-45 adds LAST x, a fifth register that quietly receives the argument of every function as it executes — so a wrong operator can be undone.

12 ENTER↑ 3 ÷
T—
Z—
Y—
X4.00
you meant −; LAST x holds 3
■ LAST x
T—
Z—
Y4
X3.00
the argument comes back
×
T—
Z—
Y—
X12.00
the division undone
■ LAST x −
T—
Z—
Y—
X9.00
the operation you meant

The lift is disabled after ENTER↑, CLx and Σ+: the next number or RCL writes over X. After anything else, including R↓ and the constant keys, a new number pushes the stack up and t falls off the top.

The function keys π, cm/in, kg/lb and ltr/gal perform an automatic ENTER↑ before delivering their constant, so 3 x² π × is the whole area calculation.

Nine registers, four of them yours without conditions

STO and RCL take a digit 1 to 9. The handbook divides the nine into unrestricted and restricted: the summation key writes into five of them and trigonometry scribbles in a sixth, so which register you pick matters.

R1free
R2free
R3free
R4free
R5n
R6Σx²
R7Σx
R8Σy
R9trig scratch

R1–R4 survive CLEAR; R5–R9 do not. Σ+ adds to R5–R8 rather than replacing them, which is why the handbook says CLEAR before every new set of data. SIN, COS, TAN, their inverses, →P and →R overwrite R9 with intermediate results.

Register arithmetic runs both ways: STO + 4 changes the register and leaves X; RCL + 4 changes X and leaves the register.

Fifteen characters, now with a choice of format

The HP-45 display is the HP-35’s — sign, ten digits, sign, two-digit exponent — but the gold FIX and SCI keys choose how much of it to show. Rounding is cosmetic: ten digits are always kept, and switching back reveals them.

signmantissa, rounded to FIX n or SCI nsignexponent−1.234567809−45FIX 2 on power-up: 123.46SCI 3: 1.235 02

In FIX a number that needs more digits than the setting allows is shown in full scientific notation, and one too small for the places shows as 0.00. The handbook counts twenty rounding options: ten FIX and ten SCI.

Two numbers in, two numbers out

Three functions return a pair: →P and →R convert between rectangular and polar, and x̄,s gives the mean and the standard deviation. In every case the first result is displayed and the second is in Y, one x⇄y away.

4 ENTER↑ 3
T—
Z—
Y4
X3.00
y then x
→P
T—
Z—
Y53.13
X5.00
r shown, θ above it
x⇄y
T—
Z—
Y5.00
X53.13
the angle
120 ENTER↑ 8 ■ →R
T—
Z—
Y6.93
X-4.00
θ then r → x, y

The order of entry mirrors the order of the results: the value that ends up in Y goes in first. →P uses R9 for scratch; the angle follows the DEG, RAD or GRD mode.

The machine

The HP-45 of 1973 is the HP-35’s machine with a shift key, and everything HP had left out to make the first one fit: nine storage registers with register arithmetic, a LAST x register, FIX and SCI display control, three angular modes, degrees-minutes-seconds, polar and rectangular conversion, mean and standard deviation, percentages, factorials, and unit constants for inches, pounds and gallons.

Same case, same red LED display, same four-level stack and the same batteries. The handbook’s opening example converts (3, 4) to polar with two keys and then shows the answer to eight places to make the point against a slide rule.

Power-up is FIX 2 and degrees, with every register cleared. The order of the two operands of y^x is reversed from the HP-35: base first, power second.

Keying in and the display

Digits, the point, CHS and EEX as on the 35. What is new is the gold FIX and SCI: a digit after either sets the number of places shown. Nothing inside is rounded.

123.456123.46 — FIX 2, the default■ FIX 4123.4560■ SCI 31.235 02■ FIX 2123.466.625 EEX 27 CHS6.625 -2750 ×0.00 — too small for FIX 2; SCI 6 shows 3.312500 -25

A number too big for its FIX setting is shown in scientific notation automatically. CLx clears the entry; gold CLEAR clears the stack and R5–R9 — but not R1–R4, which only switching off empties.

The stack and LAST x

The HP-45 has the HP-35’s four-register stack, worked the same way: ENTER↑ between two numbers you key, an automatic lift after any answer, T copied down on every drop.

12 ENTER↑ 3 ÷4.00 — but you meant to subtract■ LAST x ×12.00 — back where you started■ LAST x −9.0012 ENTER↑ 3.157 ÷ ■ LAST x × 2.157 ÷the wrong divisor replaced without re-keying 121 ENTER↑ 2 ENTER↑ 3 ENTER↑ 4 R↓review; four presses restore the stack

LAST x is the argument of the last function, saved automatically. It is the error-correction key, and also the way to reuse an argument: 12 ■ n! ■ LAST x 9 − ■ n! ÷ computes 12!/(12 − 9)! without keying 12 twice.

ENTER↑, CLx and Σ+ disable the lift for the next entry; everything else enables it.

Storage registers

STO n and RCL n, n from 1 to 9. Put an operator between STO and the digit and the arithmetic happens in the register; between RCL and the digit and it happens in X, leaving the register alone.

8 ENTER↑ 20 + 17 + 43 + STO 188.00 — the total, stored8 RCL 1 ÷0.09 — 9% of it6 STO 1 2 STO + 1 RCL 18.003 STO − 1 RCL 15.0011 RCL − 16.00 — 11 − r₁, register untouched0 STO 4 1 STO + 4 1 STO + 4a counter in R4

The handbook’s payroll example sorts hours into four registers with STO + n and then multiplies each by its rate with RCL × n — a whole quarterly report with nothing written down.

R5–R8 belong to Σ+ and R9 to the trigonometry while those are in use. R1–R4 are yours unconditionally.

Percent

% takes x percent of y and, unusually, leaves y where it was, so the net amount is one more key. Gold Δ% is the percentage change from y to x.

300 ENTER↑ 14 %42.00 — 14% of 300, and 300 is still in Y+342.00 — base plus percentage300 ENTER↑ 14 % −258.00 — base less percentage70 ENTER↑ 240 ■ Δ%242.86 — the rise, in percent

Percents are keyed as percents; there is no dividing by 100 first.

Powers, logs and factorials

Gold y^x raises the number in Y to the power in X — base first, then power, the order every HP has used since. x² is a key of its own now, with √x above it. ln and e^x are on the caps, log and 10^x above them.

2 ENTER↑ 9 ■ yx512.008 ENTER↑ 1.2567 ■ yx13.645 ENTER↑ 3 1/x ■ yx1.71 — the cube root of 54 x2 x2256.005 ■ n!120.0012 ■ n! 3 ■ n! ÷79833600.00 — twelve players in nine positions1 ex2.72

n! is defined for integers 0 to 69; anything else blinks. y^x is computed by logarithms and can miss the last digit; the handbook demonstrates this by showing 2⁹ at different FIX settings, then hides it again with FIX 2.

Trigonometry and angles

SIN, COS and TAN on the caps, their inverses above. Gold DEG, RAD and GRD set the angular mode, which lasts until changed or the machine is switched off. All of them scratch on R9.

35 COS0.82 — degrees■ RAD 6 TAN-0.29■ GRD .5 ■ SIN⁻¹33.33 — grads■ DEG .55 ■ SIN⁻¹ ■ →D.MS33.2201 — 33° 22′ 01″10.0856 ■ D.MS→ 2.1742 ■ D.MS→ + ■ →D.MS12.2638 — two survey angles added

→D.MS writes a decimal angle as dd.mmss and D.MS→ reads one back, in whatever angular mode is set; the handbook notes it works for hours, minutes and seconds too. Angles over 100,000° in either direction are improper.

To change an angle from one mode to another, convert to D.MS in the first mode and back in the second.

Polar and rectangular

→P turns x in X and y in Y into a magnitude in X and an angle in Y; gold →R turns an angle in Y and a magnitude in X back into x and y. Key the value that belongs in Y first.

4 ENTER↑ 3 →P5.00 — r; x⇄y shows the angle 53.13120 ENTER↑ 8 ■ →R-4.00 — x; x⇄y shows y, 6.93■ CLEAR 60 ENTER↑ 12 ■ →R Σ+first vector into R7 and R830 ENTER↑ 8 ■ →R Σ+second vector addedRCL Σ+ →P19.35 — the resultant; x⇄y gives 48.07°

Combining →R with Σ+ adds vectors: the x-components accumulate in R7 and the y-components in R8, and RCL Σ+ brings the sums back into X and Y for →P. The worked example below traces this through the registers.

Statistics

Gold CLEAR first, because Σ+ adds to R5–R8 rather than replacing them. Then key each value and press Σ+; the display counts the entries. x̄,s gives the mean, with the sample standard deviation one x⇄y away.

■ CLEAR 62 Σ+ 84 Σ+ 47 Σ+ 58 Σ+ 68 Σ+5.00 — n so far60 Σ+ 62 Σ+ 59 Σ+ 71 Σ+ 73 Σ+10.00■ x̄,s64.40 — the meanx⇄y10.10 — s87 Σ+ 49 Σ+ ■ x̄,s65.00 — two more ages, new mean44 ■ Σ− 47 Σ+a 44 keyed by mistake, taken out and replaced

RCL 5, 6, 7 and 8 give n, Σx², Σx and Σy; RCL Σ+ gives Σx and Σy together. A value in Y when Σ+ is pressed is summed into R8, which makes a tally: 1 ENTER↑ before the ages of the women and 0 before the men, and Σy is the number of women.

s is the sample deviation (n − 1). Multiply by √((n − 1)/n) for the population.

Unit conversions

Three constants on the digit keys 7, 8 and 9, each performing an automatic ENTER↑: key the quantity, press gold and the constant, then × for metric or ÷ for U.S. units.

3 ■ cm/in ×7.62 — inches to centimetres500 ■ kg/lb ÷1102.31 — pounds16 ■ ltr/gal ÷4.23 — gallons7 ■ ltr/gal × ■ cm/in 12 × 5280 × EEX 5 ÷ ÷16.47 — km/l to miles per gallon

The values are 2.54 cm per inch, 0.45359237 kg per pound and 3.785411784 l per U.S. gallon, all to ten digits and cited to the National Bureau of Standards.

Errors and limits

An improper operation makes the display blink; CLx, or any key that does not cause another error, stops it. The list is short and worth knowing: division by zero, y^x with a negative base, √, ln or log of a negative, 1/x of zero, n! of a non-integer, x̄,s with fewer than two entries, D.MS conversion beyond 100,000°, SIN⁻¹ or COS⁻¹ beyond ±1.

■ FIX 8 100 x2 x21.000000000 08 — too wide for FIX 8, so shown in full■ FIX 3 .000396 ENTER↑0.000 — the number is intact; FIX 6 shows it

Overflow shows ±9.999999999 99; underflow shows zero. All decimal points lit means two to five minutes of battery. Everything else about accuracy is as on the HP-35: ten digits, one count in the last place for arithmetic, a few counts of argument for the functions.

Reading more

The Owner’s Handbook (Rev. 11/74, 60 pages) is the source for this sheet, with a keyboard summary and index at the back and a stack-algorithm flowchart in Appendix A. The Quick Reference Guide is a 24-page digest that shipped in the case. Both are at literature.hpcalc.org with the HP-45 Applications book and key-sequence forms.

The HP-45 is famous for one thing the handbook never mentions: a stopwatch, left in the firmware and reachable by a key combination, which HP did not document because the crystal was not accurate enough to sell as a feature. This sheet documents only what the handbook does.

Keyboard drawn from Figure 1 of the handbook. Every keystroke sequence and result here is either the handbook’s own or was checked arithmetically.

Key & Function Index

66 entries · every key, shifted and unshifted, and every behaviour the handbook describes · hover for details and the page

Arithmetic & percent

8
+y + x; the stack drops
−y − x
×y × x
÷y ÷ x
%x percent of y — y is kept
■ Δ%percent difference from y to x
serial calculationa new number after an answer lifts the stack
chained calculationsums of products, products of sums

Entry, display & clearing

12
0 … 9 .digit keys and the decimal point
CHSchange sign
EEXenter exponent
CLxclear X
■ CLEARclear the stack and R5–R9
■ FIX nfixed decimal display, n = 0–9 places
■ SCI nscientific notation, n = 0–9 places
displayfifteen characters
9.999999999 99overflow
blinking displayimproper operation
all decimal points littwo to five minutes of battery left
OFF – ONpower switch

The stack & LAST x

6
ENTER↑copy x into Y, lifting the stack
x⇄yexchange X and Y
R↓roll the stack down
stack dropafter a two-number function
■ LAST xrecall the last argument
lift disabledafter ENTER↑, CLx or Σ+

Storage registers

7
STO nstore x in R1 … R9
RCL nrecall Rn to X
STO + nregister arithmetic: Rn + x → Rn
RCL + nx + Rn → X, register unchanged
R1 – R4unrestricted
R5 – R8the summation registers
R9scratch for trigonometry

Powers, logs & factorial

10
■ y^xy to the power x
1/xreciprocal
x^2square of x
■ √xsquare root of x
lnnatural logarithm of x
e^xnatural antilogarithm
■ logcommon logarithm of x
■ 10^xcommon antilogarithm
■ n!factorial of x, 0 to 69
■ π3.141592654

Trigonometry & angles

10
SIN · COS · TANof x in the current angular mode
■ SIN⁻¹ · COS⁻¹ · TAN⁻¹inverse functions
■ DEGdecimal degrees mode
■ RADradians mode
■ GRDgrads mode — 100 to a right angle
■ →D.MSdecimal angle to dd.mmss
■ D.MS→dd.mmss to a decimal angle
→Prectangular to polar
■ →Rpolar to rectangular
vector sums→R then Σ+, then RCL Σ+ and →P

Statistics

6
Σ+accumulate x (and y)
■ Σ−remove an entry
■ x̄,smean in X, sample standard deviation in Y
RCL Σ+Σx to X and Σy to Y
RCL 5 · 6 · 7 · 8n, Σx², Σx, Σy
a tallycount in Y, value in X

Unit conversions

3
■ cm/in2.540000000, with an automatic ENTER↑
■ kg/lb0.453592370 (avoirdupois)
■ ltr/gal3.785411784 (U.S. liquid)

Accuracy & limits

4
range10⁻⁹⁹ to 9.999999999 × 10⁹⁹
accuracyone count in the tenth digit
temperature0 to 50 °C operating
battery82001A pack, 82002A charger

Worked Example — adding two vectors with →R, Σ+ and →P

the handbook’s page 42 problem: (8 ∠ 30°) + (12 ∠ 60°), traced through the stack and the summation registers
X (shown)YR5 nR7 ΣxR8 Σy■ CLEAR0.000000the summation registers must start empty60 ENTER↑ 121260000θ first, then r■ →R6.0010.39000x = 12 cos 60°, y = 12 sin 60°Σ+1.0010.3916.0010.39x into R7, y into R8; n is displayed30 ENTER↑ 883016.0010.39the second vector■ →R6.934.0016.0010.39x = 8 cos 30°, y = 8 sin 30°Σ+2.004.00212.9314.39components addedRCL Σ+12.9314.39212.9314.39Σx to X, Σy to Y→P19.3548.07212.9314.39the resultant’s magnitudex⇄y48.0719.35212.9314.39and its angle, in degrees

The X column is the display in FIX 2; the registers are shown to the same two places. R6 accumulates Σx² throughout and is not needed here. Numbers are ten-digit values inside the machine.

Two vectors are given in polar form, 8 at 30° and 12 at 60°. Their sum is wanted in polar form too. The HP-45 has no vector keys, but it has three things that combine into one: a polar-to-rectangular conversion, a summation key that adds X and Y into registers, and a rectangular-to-polar conversion.

Clear first. Σ+ adds to R5–R8; it never resets them. Gold CLEAR empties the stack and those registers and leaves R1–R4 alone.

Each vector goes in as θ ENTER↑ r, the order →R wants: the value that lands in Y is keyed first. →R returns x in X and y in Y, and Σ+ sums x into R7 and y into R8 in one press, displaying the count so far.

RCL Σ+ is the reverse of Σ+ for the two sums: Σx to X and Σy to Y at once. That is exactly the arrangement →P wants — x in X, y in Y — so one key gives the magnitude and x⇄y the angle.

■ CLEAR 60 ENTER↑ 12 ■ →R Σ+ 30 ENTER↑ 8 ■ →R Σ+ RCL Σ+ →P19.35x⇄y48.07

Checked: 12 cos 60° + 8 cos 30° = 6 + 6.9282 = 12.9282; 12 sin 60° + 8 sin 30° = 10.3923 + 4 = 14.3923; √(12.9282² + 14.3923²) = 19.3462 and arctan (14.3923 / 12.9282) = 48.0675°.

Subtracting a vector is the same with Σ− instead of Σ+. The angular mode must be degrees for these figures; →R uses R9 for scratch, so keep nothing there.