## Early Counting Devices

### What are the early counting devices?

Early counting devices could be defined as devices used to perform arithmetic operations before the advent of modern civilization.

People learned how to count and perform arithmetic operations well back in the Stone Age. During this period, there were no complex commercial activities. People would but add, subtract, multiply and divide simple numbers. Hence, numerical operations were not as complex as it is today.

As a result, very simple devices were used in performing these simple arithmetic operations. Some of the devices used to perform arithmetic operations of those days coincide with what our children use today.

In our homes and schools, our children are taught basic arithmetic operations using these simple counting devices. But some of them have been modernized to suit the present-day educational system.

Some of the early counting devices include:

- fingers
- stones
- wooden sticks
- pebbles
- cowries
- notch sticks

In modern civilization these early counting devices have been transformed into counters, counting sticks and boxes. With these devices, our children can easily perform simple arithmetic operations. For example, it is easy for them to perform additions and subtractions by moving sticks or boxes.

Hence, it can be said that the early counting devices have not gone into complete extinction. Though there are hundreds of electronic counting devices in the market today. This implies that the early counting devices have their advantages and disadvantages. Let’s look at each of them briefly.

### Six (6) problems or disadvantages of early counting devices

What are the possible problems, limitations or disadvantages of early counting devices? Let’s consider the following obvious problems:

- They cannot be used to count large numbers. Think of using a pebble stone to perform the following addition: [2500 + 3765]. You may run out of stock. In fact, modern counting sticks and boxes are limited to a certain number.
- They are bulky. You may not be able to carry them from one place to another. Consider a situation where you need to carry 10000 pebble stones because of a business transaction. It is awkward. Even in our modern education system where sticks and boxes are used, students do not carry them up and down. They are kept in classes or store for the students to use when they come to school.
- Using them consumes a lot of time. Let us assume that you need to add up the following two numbers [379 + 578]. How long do you think it will take you to count each number before joining them together? 10mins, 15mins or 20mins? Do the same with a calculator. Can you see how terrible these devices can be in consuming your time?
- As a follow up to the above,
**it is prone to errors**. If you can use it to count large numbers, how sure are you that what you get is what it is? Imagine when you are counting up to 200 pebble stones, it is easy for you to make mistakes when distracted. Hence, it might not give us accurate results. - They are limited in scope and cannot go beyond certain numbers. As have explained above, there is a limited number of such devices you can carry at a point in time.
- Finally, they are not suitable for carrying out arithmetic operations. This is because they are very slow to use when performing operations such as additions, etc.

### Advantages or Benefits of early counting devices

- They can be used to teach basic arithmetic operations such as addition and subtractions
- They are simple to use, hence suitable for teaching children in their early years of education
- They help build up children’s intelligent quotient and memory retention capacity. Unlike the modern counting devices that store everything electronically, the ability of a child to master basic additions helps him/ her throughout life. This means that he/she can comfortably work in the absence of electronic devices.
- They are means of introducing a practical learning system in the education system. Learning by doing helps understanding and retention.

## Mechanical Counting and Calculating Devices

### Abacus

When trading between countries became important, people needed more sophisticated devices. The Abacus device was invented to replace the traditional method of counting.

The abacus device is an instrument used for counting as far back as 500 B.C. with the objective of making calculations easier, and to suit the various number systems.

In the beginning, the abacus was just a board with stones or sticks. On the surface of the abacus, there were parallel notches or grooves.

People made calculations by moving stones, sticks, bones. If numbers are to be added, stones were added, if subtraction is to be made, stones were taken off. If it were multiplication, double summing was made. When dividing, double subtraction was performed.

There are different types of abacus counting device including the Chinese abacus called *Suanpan*, invented in the 6^{th} century, the Roman abacus, named as *Calculi* or *Abaculi, and the *Japanese abacus, called *Soroban.* Soroban was used in the 16^{th} and 17^{th} century.

In China, pearls or bullets substituted stones and these were put into wire or string.

The Roman abacus was made of bronze, stone, ebony or colored glass.

### Slide Rule

In 1620, William Oughtred developed a counting device called *slide rule*. This invention was necessitated by the invention of logarithms and Napier’s bones.

This device makes use of a cursor, which is moved up and down various scales to perform multiplication and division using the principles of Logarithms. Thus, the device is equivalent to today pocket calculator.

*Mechanical Counting Devices*## Electro-Mechanical Counting Devices

### Napier’s bones

In 1617 John Napier, a Scottish mathematician, invented the Napier’s bones. These were rods on which numbers were marked.

These numbers enable the user to easily work out the answers to a restricted set of the multiplication tables. The numbers to be multiplied are positioned on the top row and the left column.

The answer is obtained at the interoperation of these two. Napier later invented tables of Logarithms which enabled multiplication and division to be carried out very simply by addition and subtraction.

### Blaise Pascal Machine

In 1642 Blaise Pascal invented the first calculating machine when he was 19 years old. This machine was developed to assist his father’s work as a government auditor of accounts.

The machine consists of clogged wheels, gears, and dials. Each wheel was divided into ten sections, representing numbers, and the mechanism allowed a carry from one wheel to the next.

This principle is still in use today. Odometers in cars use Pascal’s wheel principle to keep track of the number of kilometers traveled.

The machine had input, processing and output devices. Basically, the Pascal machine was only capable of addition.

### Gottfried Leibniz Machine

A famous German mathematician, Gottfried Von Leibniz made the most significant contribution to the mechanical calculator in 1671 when he invented the Leibniz calculating machine.

The machine can perform 4 arithmetic operations. The machine also used a wheel with teeth on them, termed “steeped wheel”, which allowed long multiplication and division to be done.

The process of multiplication involved repeated addition. Unfortunately, Leibniz’s machine was unreliable, as were most of the early calculators.

Because of this problem, mechanical calculators were not popular for many years, and it was not until the late nineteenth century that they became widely used in business.

### Joseph Jacquard Loom

The Jacquard loom is a mechanical loom, invented by Joseph Marie Jacquard in 1800. The loom simplifies the process of manufacturing textiles with complex patterns such as brocade, damask, and matelasse.

In 1725, French weaver, Basile Bouchon constructed a weaving loom that could be controlled by holes in a roll of paper. The holes allowed some needles in the loom to be engaged, while others were held back.

The loom was, therefore “programmed” by the placement of the holes in the roll of paper to produce a particular pattern. However, in Bouchon’s loom, someone had to be employed to control the needles and decide which would be used for each line of weave in the fabric.

But Joseph-Marie Jacquard improved upon Bouchon’s design by developing a loom which used a punched card to control each line of the weave. Over 1000 needles could be controlled at one time, and very intricate designs were easily created.

### Charles Babbage Analytical machine

Charles Babbage was a mathematics professor at Trinity College in Cambridge, England. After several unsuccessful attempts at building a mechanical calculating machine, Babbage developed the analytical engine in 1834.

Babbage’s designs were similar to the general design of modern-day computers, including a central arithmetic unit for calculating, called a mill, an area for retaining numbers, called a store, and sophisticated methods for input and output.

While working on his analytical engine, Babbage began a lengthy correspondence with poet Lord Byron’s daughter, Ada Augusta, Countess of Lovelace.

Lady Lovelace became fascinated with Babbage’s ideas, and in her analysis of his analytical engine, she developed the essential ideas of programming, such as “branching” to perform decisions and repetitions.

Because of her work in this area, she is considered to be the first computer programmer. The programming language “Ada” is named after her.

### Philip Emeagwali

Philip Emeagwali is a Nigerian-born engineer and computer scientist/geologist. He is called the Bill Gates of Africa. He invented the world’s fastest computer. He was one of two winners of the 1989 Gordon Bell Prize, a prize from the IEEE, for his use of a Connection Machine supercomputer to help analyze petroleum fields.

He programmed the Connection Machine to compute a world record 3.1 billion calculations per second using 65,536 processors to simulate oil reservoirs. He has submitted over 41 inventions to the US patent and trademark office.

*Images of Electro-Mechanical Counting Devices*## Electronic Counting Devices and Modern Computer

### Herman Hollerith Punch Cards

The rest of the nineteenth century witnessed the design of more complicated mechanical devices. By 1890, an American called Dr. Herman Hollerith made the most outstanding and important invention called punch cards.

The machine was used to process information obtained in the census of the population carried out in the United States in 1890. With this machine, he was able to achieve in three years what will take seven years to do manually.

Hollerith used Jacquard’s punched-card idea to feed personal statistics into his machine. Holes in the punched cards stood for a person’s age, sex, state, and other similar information. There was one card for each person.

As each card was fed into the machine, a set of metal pins were brought down on the card. The pins passed through any holes punched in the card, which completed an electrical circuit which turned a counter dial.

To sell the machine, Hollerith formed his own company in 1896, then later merged with several other companies to form the Computing Tabulating Recording Company (CTR) in 1911. CTR later became the International Business Machines or IBM.

### John Von Neumann Machine

In 1945, the Hungarian born American mathematician, John von Neumann undertook a study of computation. In this study, he demonstrated that a computer could have a simple, fixed structure, yet be able to execute any kind of computation if given properly programmed control, and without the need for hardware modification.

Von Neumann contributed a new understanding of how practical fast computers should be organized and built; these ideas, often referred to as the stored-program technique, became fundamental for future generations of high-speed digital computers and were universally adopted.

The principal feature of a von Neumann machine is that the program and any data are both stored together, usually in a slow-to-access storage medium such as a hard disk, and transferred as required to a faster, and more volatile storage medium (RAM) for execution or processing by a central processing unit (CPU).

Since this is practically how all present-day computers work, Neumann is termed the *father of the modern computer. *

The term “von Neumann architecture” is rarely used now, but it was a common parlance in the computing profession through to the early 1970s.

*Von Neuman Architecture*Prior to Neumann’s idea, programs were viewed as essentially part of the machine, and hence different from the data the machine operated on. A common approach was to input the program by some physical means, such as wiring a plugboard, and then feeding in the data for the program to act upon.

As a result of Neumann’s discovery, computing and programming became faster, more flexible, and more efficient, with the instructions in subroutines performing far more computational work.

In 1945, von Neumann proposed the stored program concept in his report on the EDVAC. He did it together with computer pioneers, J. Presper Eckert, John Mauchly, Arthur Burks, and Hermann Goldstine, who was working on plans for the EDVAC.

According to the original papers proposing the new architecture, a von Neumann computer has five parts: **an arithmetic-logic unit, a control unit, a memory, some form of input/output, and a bus** that provides a data path between these parts. Such a computer operates by performing the following sequence of steps:

- Fetch the next instruction from memory at the address in the program counter.
- Add the length of the instruction to the program counter.
- Decode the instruction using the control unit.
- Go back to step 1.

Von Neumann computers have some drawbacks. In particular, they carry out instructions one after another, in a single linear sequence, and they spend a lot of time moving data to and from the memory. This slows the computer. This problem is called the *von Neumann bottleneck*.

### Modern machines

The EDVAC computer, when it was finally constructed in 1952, followed von Neumann’s design. But the first von Neumann computer to be constructed and operated as the Manchester Mark I.

*Manchester Mark 1*This machine was designed and built at Manchester University in England. It ran its first program in 1948. The computer had a 96-word memory and executed an instruction in 1.2 milliseconds. Today, the computer you are using is born out of von Neumann’s idea.

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