How do computers use binary to process data
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.
A standard Binary Coded Decimal , an enhanced format of Binary Coded Decimal, is a 6-bit representation scheme which can represent non-numeric characters. This allows 64 characters to be represented. A total of 2 8 characters can be coded using this scheme.
For example, the symbolic representation of letter A using Extended Binary Coded Decimal Interchange code is 2. However, manufactures have added an eight bit to this coding scheme, which can now provide for characters. This 8-bit coding scheme is referred to as an 8-bit American standard code for information interchange.
The symbolic representation of letter A using this scheme is In mathematics, the four basic arithmetic operations applied on numbers are addition, subtraction, multiplications and division. In computers, the same operations are performed inside the central processing unit by the arithmetic and logic unit ALU. However, the arithmetic and logic unit cannot perform binary subtractions directly. It performs binary subtractions using a process known as For multiplication and division, the arithmetic and logic unit uses a method called shifting before adding the bits.
Representation of signed binary numbers In computer technology, there are three common ways of representing a signed binary number. Prefixing an extra sign bit to a binary number. For example, the 7-bit binary equivalent of is 2. To indicate that it is positive, we add an extra bit 0 to the left of the number i.
To indicate that it is negative number we add an extra bit 1 i. The problem of using this method is that the zero can be represented in two ways i.
The term compliment refers to a part which together with another makes up a whole. For example in geometry two complimentary angle 90 0. The idea of compliment is used to address the problem of signed numbers i.
Other numeral systems exist because there are specific uses where a certain numeral system is easier to use and offers advantages over another. Binary and hexadecimal numbers are widely used in computer science. Binary numbers can be considered the very basic representation of a number in an electronic device.
This will help to explain why binary numbers are so important. The very first computers used binary numbers, and they are still used today. Every computer is made up of many electronic components. That is why a basic knowledge of electronics is needed to understand how and why binary numbers are used in computers. A computer is built with many connections and components, which are used to transfer and store data, as well as communicate with other components.
Most of that storing, transferring, and communicating happens with digital electronics. In electronics, a voltage level or current flow is a way to represent a value. For example, 5V volts or 0. The makers of electronic devices could, of course, assign any meaning that they want to different voltage values. You would end up with 0. This means that when building an electronic device, it is most often desired to have the energy consumption as low as possible and to have a low voltage.
Furthermore, electronic signals are not always very steady and can vary because of surrounding influences, like nearby internal circuits for other electronic devices.