SS1 Second Term Further Mathematics Lesson Note – Calculating and Processing Devices

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WEEK 3

TOPIC:   CALCULATING AND PROCESSING DEVICES

CONTENT:

1. Calculating devices (Abacus, Slide Rule, pocket Calculator and the Computer)
2. Decimal, binary, octal, hexadecimal systems and relationship between them
3. Flow charts
4. Application of flow – chart

Sub – Topic: CALCULATING DEVICES

Calculating devices are those manual methods and machines for speeding up calculations have been devised. One of such devices that uses a positional numeration system is the abacus. Others include lattice or gallery method, slide rule invented by william oughtred, Russian peasant method, Egyptian multiplication algorithm, John Napier logarithms, etc. All the afore-mentioned and many others not mentioned were existing and ruling the world of calculation before the invention of pocket, desk and electronic calculators, computers and the other sorted modern calculating machines. It is worth noting that, all the modern calculating machines today were build up on the existing ancient calculating and processing devices. For example, from the works of John Von Neumann in 1946, attempt was made to develop the digital computer, where a programmer can compose a few instructions, enter them into the computer memory, and then watch while it performs millions of calculations on its own and reports the answers.

ABACUS-CALCULATING DEVICE

Abacus, instrument used in performing arithmetic calculations. It consists essentially of a tablet or frame bearing parallel wires or grooves on which counters or beads are moved. A modern abacus consists of a wooden frame with beads on parallel wires, and a crossbar oriented perpendicular to the wires that divides the beads into two groups. Each column—that is, each wire—represents one place in the decimal system. The column farthest to the right is the ones column; the next column to the left is the tens column; and so on. In each column, there are five beads below the crossbar, each of which represent one unit, and two beads above the crossbar, each of which represent five units. For example, in the ten’s column, each of the group of five beads represents ten, and each of the group of two beads represents fifty. Beads that are to be counted as part of a number are placed against the crossbar. Abacus is used in places like China and Japan. Addition and subtraction are performed by movement of beads from side to side for:

• adding or removing beads
• Repeated addition is done with the abacus for multiplication.

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