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Calculators: What do keys and switches on vintage calculators do?

Key

Name Where Function

All Clear Common All Clear.  This key is usually seen in conjunction with a (C) clear/cancel to clear the last entry.  The all clear function clears all registers but usually leaves the memory store intact.  The result of pressing AC is usually "0" as the calculator is ready to start a new calculation. 

Clear or Cancel Common This key will be used for Cancel last entry if (AC) is present or for Cancel if associated with a (CE) key.

Clear/Cancel Entry Common This two function key is pressed once to cancel a number entered and a second time to clear the calculator in total.  For instance, keying in (5)(X)(2)(CE)(3)(=) results in 15 (5 X 3) as the answer.  

Cancel Entry Common This key is pressed to cancel a number entered.  For instance, keying in (5)(X)(2)(CE)(3)(=) results in 15 (5 X 3) as the answer.  

LSD 1974/5 Allows you to see the least significant digits.  On a six digit display this will show the six further digits to the right of your displayed number.  The display reverts to normal when the key is released.  Not only did this allow extra precision (in some cases up to 16 digits) but it kept the costs (and power requirement) down on early calculators by reducing the number of required display digits.

Register exchange Hanimex When operating the constant function this will swap the contents of the display with the constant register.  This means the "answer" becomes the constant operator.  Can also be used to swap the contents of the memory register in conjunction with the (M) key.

Register exchange Imperial /
Adler
As above but not used for memory exchange.

EXchange register Brother As above but not used for memory exchange.

Percentage Common Probably the most common, and in the early days most variable, extra calculator function.  Usually used in conjunction with the multiply key; (5)(0)(X)(1)(0)(%)(=) results in 5 (10% of 50), pressing (-) then will result in 45 (as it discounts the original 50 by the 10%.  However, in some early calculators I have seen this button just divide by 100.
Change Sign Common Allows you to change the number you are inputting from positive to minus and back.  Can also be used to change the sign of the result on display.  Some early calculators do not allow you to change sign in mid-entry or before equals is pressed.  Can cause an overflow situation where a calculator uses one of the number display digits for the minus sign; i.e. trying to make an eight digit number negative will not fit on the display.

Change Sign Imperial /
Adler
Same as the change sign above.  Somewhat confusing key label as this sort of thing was later used on scientific calculators to enter brackets.
Pi Common This Greek letter stands for the useful constant that is the ratio between a circle's diameter and circumference.  Pressing this number usually brings up 3.1415926.
Square Root Common Produces that number, that when multiplied by itself, will generate the original number again.  Pressing (9)(SQR) shows 3 (as 3x3=9).  Non integer results usually show a rounding error, e.g. is you try (2)(SQR) you will get 1.4142135.  If you try and square this (by using (X)(=)) you will get something like 1.9999998.

Square Usually Scientific Does the reverse of the square root by multiplying the number by itself.  Typing (3)(X2) results in "9" without having to press the (=) key.  See note on rounding errors under Square Root.

Total accumulated Sperry Shows the total that has been accumulated (added) into the memory since the last clearing operation.  Usually this accumulation is automatic on every press of the (=) key.

Memory function Common When you see the (M) key in isolation it is usually used as part of a two key sequence. Either (M) is used like a "function shift" key and invokes the "uppercase" function (such as M+) or it is used in conjunction with the standard operator keys (like (+)(=) or (X)) in the same way.  This idea reduces the number of keys needed for memory functions.

Cancel memory Common Clears the memory to the value zero.  Will switch off any display element that tells you that memory is stored.  The same result can be usually obtained by subtracting the same amount that is stored in the memory.

Recall Memory Common Will return the value in the memory and not delete the memory. if the memory is equal to 10 then (5)(X)(RM)(=) results in 50.
Memory recall / cancel Common The first press of the key will recall the content s of memory, the second consecutive press will clear the memory

Memory Out Imperial /
Adler
Same as recall memory above.

Add to memory Sometimes Will simultaneously conclude the current calculation and add the result to the memory.  Often the same as the (M+) key but occasionally this may add only the display amount)
Add to memory Common Adds whatever is on the display to the current contents of the memory
Subtract from memory Common Subtracts whatever is on the display to the current contents of the memory

Switches

Financial input Occasional early Mostly seen on desktops this sort of function is ideal for rapid financial input.  Switching this function in assumes that every input has two decimal places.  Keying in (3)(4)(5) results in the input of 3.45 - ideal for adding together amounts of money quickly.

Decimal switch Early and desktop There are many varieties of this switch, the particular example show combines the on/off switch but it was as often a separate switch.  You may see any number ranging from zero to ten which "fixes" the decimal point display to be that many digits.  The "F" setting stands for "Floating decimal point" i.e. the necessary number of decimal points is used automatically.