Knowledge & Memory

The Pascaline and the Step Reckoner as Decimal Digital Arithmetic Engines

Period and origin

Pascal from the 1640s; Leibniz’s stepped-drum principle later in the same century

What it was built to do

To mechanise decimal digit state and carry, for administrative arithmetic and then for repeated addition with positional shifting.

How the mechanism works

An n-digit register is a physical state vector of decimal wheels. Input wheels add increments and trigger carry mechanisms. In a stepped reckoner the axial position of a gear selects how many teeth of a stepped drum engage, adding a chosen digit repeatedly to an accumulator, while carriage displacement multiplies by powers of ten.

Input

Digits entered on the input wheels, and a carriage position.

Transformation

Digitwise addition with carry propagation; repeated addition and positional shift for multiplication.

Output

The accumulator’s decimal state, read directly off the register.

What is evidenced

Established: the artefact or the documentary record carries this directly.

What it demonstrates

Physical positional registers, carry propagation, and the separation between operand entry and accumulator state - and that these are not general-purpose programmable computers.

All mechanisms