EARLY MECHANICAL COUNTING DEVICES

 EARLY MECHANICAL COUNTING DEVICES

Man has put in every effort to have better methods of calculations. As a result of man’s search for fast and accurate calculating devices, the computer was developed. Essentially, there are three kinds of calculating devices: manual, mechanical and automatic.

 

EARLY MECHANICAL COUNTING/CALCULATING DEVICES

1. Abacus

2. Slide rule

 

EARLY ELECTRO-MECHANICAL COUNTING DEVICES

1. John Napier bone

2. Blaize Pascal machine

3. Gottfried Leitbnitz machine

4. Joseph Jacquard Loom

5. Charles Babbage analytical machine

 

EARLY ELECTRONIC COUNTING DEVICES:

1. Herman Hollerith punch card

2. John Von Neumann machine

ABACUS

The first calculating device was probably Abacus. The Chinese invented it. It is still in use in some countries because of its simple operation. It is made up of a frame divided into two parts by a horizontal bar and vertical threads. Each thread contains some beads. It was used to calculate simple addition and subtraction.

NAPIER’S BONE

 John Napier, a Scottish mathematician, invented a set of eleven rods, with four sides each which was used as a multiplication tool. These rods were made from bones and this was the reason why they were called Napier Bones. The rods had numbers marked in such a way that, by placing them side by side, products and quotients of large numbers can be obtained.

PASCALINE

The first mechanical calculating machine was invented in 1642, by Blaize Pascal, a French mathematician. Numbers were entered by dialling a series of numbered wheels in this machine. A sequence of wheels transferred the movements to a dial, which showed the result. 

Through addition and subtraction were performed the normal way, the device could perform division by repeated subtraction and multiplication by repeated addition.

LEIBNITZ CALCULATING MACHINE

Gottfried Wilhelm Von Leibnitz invented a computer that was built in 1694. It could add and after changing some things around, it could multiply. Leibnitz invented a special stepped gear mechanism for introducing the added digits and this is still being used.

JACQUARD’S LOOM

Jacquard’s loom was one of the first machines that were run by a program. Joseph Jacquard changed the weaving industry by creating a loom that controlled the raising of the thread through punched cards. Jacquard’s loom used lines of holes on a card to represent the weaving pattern.

PUNCHED CARD

During the years 1920 and 1930, the punched card system developed steadily. A standard card was divided into 80 columns and 12 rows. Only one character could be represented in the 80 columns, thus providing a maximum of 80 characters per card. Punching one, two or three holes in any one column represented a character. Holes were punched into a blank card by a punch machine whose keyboard resembled that of a typewriter.

Number system

 Number system is a way to represent numbers we are used to using the Base - 10 number system, which is also called decimal.

Other common number systems includes

Base 2 - Binary system

Base 8 - Octal system

Base 16 -  Hexadecimal system

THE BASE 10 OR DECIMAL NUMBER SYSTEM

This is known as Decimal or Base 10, it is the number we use everyday. It uses 10 numerals or pictures to represent all of the possible numbers that can be form in the base 10 number system

The numerals are 0,1,2,3,4,5,6,7,8 and 9.

CONVERSION OF NUMBERS IN BASE 2 TO NUMBER IN BASE 10

Consider the natural number or base 10 number 456 or 456_10. It is four hundred and fifty six in base ten. The number can be written as:

400 + 50 + 6

 (4x100) + (5x10) + (6x1)

 (4x10²) + (5x10¹) + (6x10⁰)

Note that the value of a number raised to power zero is one i.e 10⁰ = 1, 2⁰ = 1, 8⁰ = 1, e.t.c

.For a base 2 number 1101₂

The extended form of the number becomes:

(1x2³) + (1x2²) + (0x2¹) + (1x2⁰)

: Hexadecimal number system

The Hexadecimal Number System consists of 16 digits from 0 to 9 and A to F. The alphabets A to F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position in hexadecimal system represents a power of 16, the digits involve are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. The letter A,B,C,D,E,F represent 10,11,12,13,14,15 respectively.  

Convert the following hexadecimal numbers to decimal

5B₁₆

A4F₁₆

Solution

5B₁₆

 

161	160
5	B

 

The expanded form is:

(5x16¹) = (Bx16⁰)

(5x16) + (11x1)

80 + 11

91₁₀

 

A4F₁₆

162	161	160
A	4	F

 

The expanded form is:

(AX16²) + (4X16¹) + (FX16⁰)

(10X16²) + (4X16¹) + (15X16⁰)

(10X256) + (4X16) + (15X1)

2560 + 64 + 15

2639₁₀