Brief Notes of Number System and Conversion (Computer) for Paper 1
Followings are the main memory storage units:
|1||Bit(Binary Digit)||A binary digit is logical 0 and 1 representing a passive or an active state of a component in an electric circuit.|
|2||Nibble||A group of 4 bits is called nibble.|
|3||Byte||A group of 8 bits is called byte. A byte is the smallest unit which can represent a data item or a character. (1 byte = 8 bits)|
|4||Word||A computer word, like a byte, is a group of fixed number of bits processed as a unit which varies from computer to computer but is fixed for each computer. The length of a computer word is called word-size or word length and it may be as small as 8 bits or may be as long as 96 bits. A computer stores the information in the form of computer words.|
Few higher storage units are following:
|1||Kilobyte (KB)||1 KB = 1024 Bytes|
|2||Megabyte(MB)||1 MB = 1024 KB|
|3||GigaByte (GB)||1 GB = 1024 MB|
|4||TeraByte (TB)||1 TB = 1024 GB|
|5.||PetaByte (PB)||1 PB = 1024 TB|
|1000000 (1 Million)||1MB|
|1000000000000 (1 Trillion)||1 TB|
When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.
A value of each digit in a number can be determined using
- The digit
- The position of the digit in the number
- The base of the number system (where base is defined as the total number of digits available in the number system).
- Decimal Number System: The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands and so
- Binary Number System: Uses two digits, 0 and 1, also called base 2 number system . Each position in a binary number represents a 0 power of the base (2). Last position in a binary number represents a x power of the base (2).
- Octal Number System: Uses eight digits, 0,1,2,3,4,5,6,7, also called base 8 number system, Each position in an octal number represents a 0 power of the base (8).
- Hexadecimal Number System: Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Letters represents numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15. Also called base 16 number system .Each position in a hexadecimal number represents a 0 power of the base (16).Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Letters represents numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15. Also called base 16 number system .Each position in a hexadecimal number represents a 0 power of the base (16).
There are many methods or techniques which can be used to convert numbers from one base to another.
We’ll demonstrate here the following
- Decimal to Binary System
- Binary to Decimal
Decimal to Binary System
Step 1 – Divide the decimal number to be converted by the value of the new base.
Step 2 – Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number.
Step 3 – Divide the quotient of the previous divide by the new base.
Step 4 – Record the remainder from Step 3 as the next digit (to the left) of the new base number.
Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3. The last remainder thus obtained will be the most significant digit (MSD) of the new base number.
Decimal Number: (29)10
Calculating Binary Equivalent:
|Step 1||29 / 2||14||1|
|Step 2||14 / 2||7||0|
|Step 3||7 / 2||3||1|
|Step 4||3 / 2||1||1|
|Step 5||1 / 2||0||1|
As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the least significant digit (LSD) and the last remainder becomes the most significant digit (MSD).
Decimal Number: 29 = Binary Number: 11101
Binary to Decimal System
Step 1 – Determine the column (positional) value of each digit (this depends on the position of the digit and the base of the number system).
Step 2 – Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.
Step 3 – Sum the products calculated in Step 2. The total is the equivalent value in decimal.
Binary Number: 111012
Calculating Decimal Equivalent:
|Step||Binary Number||Decimal Number|
|Step 1||(11101)2||((1 x 24) + (1 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10|
|Step 2||(11101)2||(16 + 8 + 4 + 0 + 1)10|
Binary Number: 11101 = Decimal Number: 29
Sign of Decimal – ( )10 and Binary ( )2
(Note : this study material is provided by UCADEMIC INSTITUTE)