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Computer Architecture


A)


1) The Arabic method of representing numbers that is in common use today is decimal, which is based on the number ten. Within decimal we use the numbers 0 to (also known as symbols); we use these symbols to display value. Hence in decimal the value is equal to the symbol and its position.


However the Roman system of numbering is based on letters (also know as characters). Within Roman they used the characters I, V, X, L, C, D&M. Because this is not a Base system it makes arithmetic very difficult. As well as this within Roman there is no way to represent zero and no way to represent negative numbers.


Cheap University Papers on Computer Architecture HNC Computing




) Base two is known as binary this is represented by the digits 1 & 0, each number 1 or 0 is known as a bit.


An example of binary would be () () (1) (0)


8 4 1


1 1 1 1


(18) + (14) + (1) + (11) = 15


Base 16 is known as Hexadecimal (Hex) this is represented by the digits 0- and the letters A-F with A = 10 and F= 15


1 A B


=(156) + (1016) + (111)


= 56 + 160 + 11 = 47


An example of Hex would be


) The relationship between Binary and Hexadecimal is nibbles this is four binary digits or half of an eight-bit byte. A nibble can be conveniently represented by one hexadecimal digit. To distinguish between Hexadecimal and decimal an H is placed after the hexadecimal number.


Below is an example of the relationship between Binary and Hexadecimal


8 4 1 / 8 4 1 (decimal)


1 0 1 0 / 1 1 0 1 (binary)


=10 (A) / = 1 (D) = A D H (Hex)





B)


Computers are digital devices that at their basic level they can only recognise just two states. Because the computer uses voltage levels these are +5V and 0V (+/- or on/off). Binary is the easiest form for the computer to use. This is however not the easiest form for users to view, as a computer can handle very large numbers. To try to eliminate human error a different base system (hexadecimal) is used, this makes it easier for the user to read and the computer to convert.


Bit


A bit (short for binary digit) is the smallest unit of data in a computer. A bit has a single binary value, either 0 or 1.


Byte


A byte is a unit of data that is eight binary digits long. A byte is the unit most computers use to represent a character such as a letter or number.


Word


A Word is a group of bits which is treated by the computer as a single unit for retrieving, processing and storing; it is not a fixed amount. So for example a -bit processor uses -bit words, this is the number of digits that are transmitted along its data bus in one clock cycle.


C)


Ways in which computers are able to store and manipulate data such as text, pictures and numbers are ASCII, Bitmap and Vector.


ASCII (American Standard Code for Information Interchange)


ASCII was developed by the American National Standards Institute and is recognised world wide. It is used for storing letters, numbers, characters and symbols. Each of these is represented with a seven bit binary number (a string of 7 0s or 1s), and is given a unique number. An example of which would be K=75 and k=107, there are 18 possible character definitions.


Bitmap


This is an image in which every pixel (dot) on the screen or in the image is mapped to a bit of data. With a monochrome picture there is a direct connection between the number of screen pixels and the number of bits to store the picture. As each bit only stores whether the picture is black or white. Whereas with colour pictures each pixel is represented by groups of bits that will determine the pixels colour.


The problem with bitmaps is that not only do they use a lot of storage space, but the quality of the image can become distorted when increasing the size of the image (because it is stored in pixels).


Vectors


Vector graphics is the creation of digital images through a sequence of commands or mathematical statements that place lines and shapes in a given two-dimensional or three-dimensional space. Vector images are easier to manipulate than bit-mapped images as they can be resized and stretched without distortion of the image (as they are not saved in pixels).


As well as this they require less storage space than bit-mapped images.





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