1.1 NUMBER SYSTEM
A number system relates quantities and symbols. In digital system how information is
represented is key and there are different radices, i.e. number bases, which a numbering
system can use.
The memory unit stores programs as well as input, output and intermediate data. The
processor unit performs arithmetic and other data processing tasks as specified by the
program. The control unit supervises the flow of information between various units. The
program and data prepared by the user are transferred into the memory unit by means of an
input device such as punch card reader (or) tele typewriter. An output device, such as printer,
receives the result of the computations and the printed results are presented to the user.
It can have different base values like: binary (base-2), octal (base-8), decimal (base 10) and
hexadecimal (base 16), here the base number represents the number of digits used in that
numbering system. As an example, in decimal numbering system the digits used are: 0, 1, 2,
3, 4, 5, 6, 7, 8 and 9. Therefore the digits for binary are: 0 and 1, the digits for octal are: 0,
1, 2, 3, 4, 5, 6 and 7. For the hexadecimal numbering system, base 16, the digits are: 0, 1,
2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Numbers that contain only two digit 0 and 1 are called Binary Numbers. Each 0 or 1 is called
a Bit, from binary digit. A binary number of 4 bits is called a Nibble. A binary number of 8
bits is called a Byte. A binary number of 16 bits is called a Word on some systems, on others
a 32-bit number is called a Word while a 16-bit number is called a Halfword.
Using 2 bit 0 and 1 to form
a binary number of 1 bit, numbers are 0 and 1
a binary number of 2 bit, numbers are 00, 01, 10, 11
a binary number of 3 bit, such numbers are 000, 001, 010, 011, 100, 101, 110, 111
a binary number of 4 bit, such numbers are 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111,
1000,
1001, 1010, 1011, 1100,1101,1110,1111
Therefore, using n bits there are 2
n
binary numbers of n bits
Each digit in a binary number has a value or weight. The LSB has a value of 1. The second
from the right has a value of 2, the next 4 , etc.,
Table 1.1 Binary Weights