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Optical devices use this technology to read or store data. Take example of a CD-ROM, if the shiny surface is placed under a powerful microscope, the surface is observed to have very tiny holes called pits. The areas that do not have pits are called land. Consists of eight digits ranging from Hexadecimal number system This is a base 16 number system that consists of sixteen digits ranging from and letters A-F where A is equivalent to 10,B to 11 up to F which is equivalent to 15 in base ten system.
The place value of hexadecimal numbers goes up in factors of sixteen. When converting a real number from binary to decimal, work out the integral part and the fractional parts separately then combine them.
Working from left to the right, each octal number is represented using three digits and then combined we get the final binary equivalent. The binary equivalent of the fractional part is extracted from the products by reading the respective integral digits from the top downwards as shown by the arrow next pag. To convert binary numbers to their binary equivalents, simply group the digits of the binary number into groups of four from right to left e.
The next step is to write the hexadecimal equivalent of each group e. The simplest method of converting a hexadecimal number to binary is to express each hexadecimal digit as a four bit binary digit number and then arranging the group according to their corresponding positions as shown in example.
The main purpose of using ones compliment in computers is to perform binary subtraction. For example to get the difference in 5 — 3, using the ones compliment, we proceed as follows:. Like in ones compliment, the twos compliment of a number is obtained by negating a positive number to is negative counterpart.
For example to get the difference in , using twos compliment, we proceed as follow:. Computers are classified according to functionality, physical size and purpose. Functionality, Computers could be analog, digital or hybrid. Digital computers process data that is in discrete form whereas analog computers process data that is continuous in nature.
Hybrid computers on the other hand can process data that is both discrete and continuous. In digital computers, the user input is first converted and transmitted as electrical pulses that can be represented by two unique states ON and OFF. Although the two graphs look different in their appearance, notice that they repeat themselves at equal time intervals.
Electrical signals or waveforms of this nature are said to be periodic. Generally,a periodic wave representing a signal can be described using the following parameters Amplitude A Frequency f periodic time T Amplitude A: It is measured in hertz. When a digital signal is to be sent over analog telephone lines e. This is done by connecting a device called a modem to the digital computer. This process of converting a digital signal to an analog signal is known as modulation.
On the receiving end, the incoming analog signal is converted back to digital form in a process known as demodulation. Data and instructions cannot be entered and processed directly into computers using human language. Any type of data be it numbers, letters, special symbols, sound or pictures must first be converted into machine-readable form i.
Due to this reason, it is important to understand how a computer together with its peripheral devices handles data in its electronic circuits, on magnetic media and in optical devices. Data representation in digital circuits Electronic components, such as microprocessor, are made up of millions of electronic circuits.
This concept can be compared to switching on and off an electric circuit. This forms a basis for describing data representation in digital computers using the binary number system. Data representation on magnetic media The laser beam reflected from the land is interpreted, as 1. The laser entering the pot is not reflected. This is interpreted as 0. The reflected pattern of light from the rotating disk falls on a receiving photoelectric detector that transforms the patterns into digital form.
Magnetic technology is mostly used on storage devices that are coated with special magnetic materials such as iron oxide. It has proved difficult to develop devices that can understand natural language directly due to the complexity of natural languages. All forms of data can be represented in binary system format. Other reasons for the use of binary are that digital devices are more reliable, small and use less energy as compared to analog devices.
Bits, bytes, nibble and word The terms bits, bytes, nibble and word are used widely in reference to computer memory and data size. It is the basic unit of data or information in digital computers. A byte is considered as the basic unit of measuring memory size in computer.
The term word length is used as the measure of the number of bits in each word. For example, a word can have a length of 16 bits, 32 bits, 64 bits etc. Computers not only process numbers, letters and special symbols but also complex types of data such as sound and pictures. However, these complex types of data take a lot of memory and processor time when coded in binary form. This limitation necessitates the need to develop better ways of handling long streams of binary digits.
Higher number systems are used in computing to reduce these streams of binary digits into manageable form. This helps to improve the processing speed and optimize memory usage. Number systems and their representation A number system is a set of symbols used to represent values derived from a common base or radix. As far as computers are concerned, number systems can be classified into two major categories: Decimal number system has ten digits ranging from Because this system has ten digits; it is also called a base ten number system or denary number system.
A decimal number should always be written with a subscript 10 e. X 10 But since this is the most widely used number system in the world, the subscript is usually understood and ignored in written work. However ,when many number systems are considered together, the subscript must always be put so as to differentiate the number systems. The magnitude of a number can be considered using these parameters.
Absolute value Place value or positional value Base value The absolute value is the magnitude of a digit in a number. The place value of a digit in a number refers to the position of the digit in that number i. The total value of a number is the sum of the place value of each digit making the number. The base value of a number also k known as the radix , depends on the type of the number systems that is being used.
The value of any number depends on the radix. It uses two digits namely, 1 and 0 to represent numbers. Octal number system Consists of eight digits ranging from A hexadecimal number can be denoted using 16 as a subscript or capital letter H to the right of the number.
For example, 94B can be written as 94B16 or 94BH. Further conversion of numbers from one number system to another To convert numbers from one system to another. Converting between binary and decimal numbers. Converting octal numbers to decimal and binary form. Converting hexadecimal numbers to decimal and binary form. First, write the place values starting from the right hand side.
Write each digit under its place value. Multiply each digit by its corresponding place value. Add up the products. The answer will be the decimal number in base ten. The binary equivalent of the fractional part is extracted from the products by reading the respective integral digits from the top downwards as shown by the arrow next page.
Combine the two parts together to set the binary equivalent. Solution Convert the integral and the fractional parts separately then add them up. For the fractional part, proceed as follows: Multiply the fractional part by 2 and note down the product Take the fractional part of the immediate product and multiply it by 2 again. Continue this process until the fractional part of the subsequent product is 0 or starts to repeat itself. The following examples illustrate how to convert hexadecimal number to a decimal numberExample Convert octal number 8 to its binary equivalent Solution Working from left to the right, each octal number is represented using three digits and then combined we get the final binary equivalent.
Converting hexadecimal numbers to decimal number To convert hexadecimal number to base 10 equivalent we proceed as follows: However, it is important to note that the maximum absolute value of a octal digit is 7. For example Is not a valid octal number because digit 9 is not an octal digit, but 8 is valid because all the digits are in the range Example shows how to convert an octal number to a decimal number.
Octal digit Binary equivalents 0 1 2 3 4 5 6 7 Example Convert the hexadecimal number 16 to its binary equivalent. Solution Place each number under its place value. In computing, a single character such as a letter, a number or a symbol is represented by a group of bits.
The number of bits per character depends on the coding scheme used. The most common coding schemes are: For example, a number like 9 can be represented using Binary Coded Decimal as 2. Binary Coded Decimal is mostly used in simple electronic devices like calculators and microwaves. This is because it makes it easier to process and display individual numbers on their Liquid Crystal Display LCD screens.