Number Systems Flashcards
Why computers use binary data?
Because computers are made up of billions of transistors (tiny switches) which are either in the ON state represented by the binary digit 1 or the OFF state represented by the binary digit 0. The base 2 number system is the perfect use for this purpose.
What is the denary number system?
It is a base 10 number system, normally known as the decimal number system.
What is the binary number system?
It is a base 2 number system. It is used for computing. Computers only understand binary.
What is the hexadecimal number system?
It is a base 16 number system. It is used by programmers etc. Because of its ease of use as it is 4 times shorter than binary.
How to convert from base 2 to bases 10 and 16.
To convert from base 2 to 10, we need to see which binary place values represent the ON state I.e: 1. Then we add all the place values of the ON state. To convert from base 2 to 16, we first divide the binary in groups of 4 each (as base 16 is 4 times base 2), after the grouping we just convert the binary to base 10 and then join all the numbers afyer converting them into base 16 based numbering.
How to convert from base 10 to base 2 and 16?
To convert from base 10 to 2, we can use the successive subtraction method where we subtract the number by the biggest possible place value of base 2 until 0 is achieved, and then mark all place values used in subtraction as 1 and others as 0. Or we can use the successive division method where we are supposed to divide the number by 2 until 0 is reached and write the remainders during the process. Then flip the position of all the remainders from end to start to get the converted number. To convert from base 10 to 16, we use the same successive division method but instead divide the number by 16 and not 2.
How to convert from base 16 to 2 and 10?
To convert from base 16 to 2, we write all base 16 numbers individually and then use the successive subtraction or successive division method for each number. To convert from base 16 to 10, we first write all base 16 numbers individually, then multiply them with their respectful place values, then add all the products together to get the base 10 number.
What are some uses of the base 16 system in computers?
They are used in error codes, MAC Addresses, IPv6 addresses and HTML Color Codes
What are error codes?
These are the memory location of the error, they allow to trace errors during program development.
What are MAC Addresses?
They are numbers which uniquely identify a network device. It refers to the Network Interface Card which is a part of the device. It is usually 48bits but in some cases it is 64bit as well. It is in 6 groups of two hex digits. The first 3 groups (first half) is the identity number of the device manufacturer and the second half is the serial number of the device.
What are Internet Protocol (IP) Addresses?
They are the addresses given to any device connected to a network for communication purposes. There are now two types of IP Addresses, IPv4 and IPv6. IPv4 is a 32 bit address while IPv6 is a 128 bit address. IPv4 is represented in denary form and IPv6 is represented in hexadecimal form grouped into 16bit chunks. IPv6 uses a colon as a chunk seperator instead of a decimal point.
What is the relation of HTML with Hex?
HTML is a mark up language used to represent text on a computer. In HTML text can be given colors, and, the color codes are coded in hexadecimal. Where each color spectrum has two hex values which make up 256 values each. As we have 3 basic colors, the total amount of colors available to us are 16,777,216.
What is an overflow error?
An overflow error is the error which is produce when a number bigger than the bit size of the register is used resulting in overflow of the register.
What is a logical shift?
A logical shift is moving the binary number to the left or right. Moving left is basically multiplying it by 2 and moving right is basically dividing it by 2.
What is two’s complement?
It is a way of representation for binary numbers where the left most place value is changed to a negative value. A 1 value in the left most bit represents a negative number and a 0 represents a positive number.
