Because of the many papers that teachers must grade, it sometimes develops that a problem solved incorrectly is checked quickly by the teacher as wrong, and returned to the pupil without the teacher’s having had a sufficient opportunity to know what the pupil was thinking when he did the problem. Some errors may be classified as pure carelessness, but in other cases there may be some basic fundamentals that the pupil has not grasped, and these are important to clarify

Digital Computers can be thought to have 3 parts, the memory, which stores numbers and instructions, the arithmetic unit, which does the arithmetic, and the control, which selects, interprets, and acts upon the instructions. Numbers are fed into the machine by some means such as paper tape, which is prepared by a device like a typewriter. The instructions are put on the tape in a coded form, and may look like something like this:

A certain type of transformation of a set of numbers may be represented as the multiplication of a vector by a square matrix. Repetition of the operation is equivalent to multiplying the original vector by a power of the matrix. Properties of powers of matrices are thus of considerable importance, and many general properties have been established for some time.

Nowadays, when so much computing is done with the use of the binary scale, it is arguable that some knowledge of binary arithmetic should be part of the mathematical equipment of the normal grammar-school pupil. The basic electric circuits for binary addition are comparatively simple, and a satisfactory machine for demonstrating the principles can be constructed with standard multiple switches and a flash-lamp battery and bulbs. In the U.S.A. the progressive firm of Berkeley Enterprises, Inc., of Newtonville Mass. has popularized “Geniac” kits from which various simple computing devices can be manufactured from interchangeable components. I am indebted to the Geniac Manual for some of the basic circuits I have used, though I have modified them considerably