3. Number System means the way to represent the various types
of numbers .
Example: A number 152 pronounced as One Hundred Fifty
Two.
The Base of a number system is the number of different digits
Which can occupy each position of the system.
4. These are of following types:
(1) Binary Number System
(2) Decimal Number System
(3) Hexadecimal Number System
(4) Octal Number System
5. The Binary Number System uses only two numbers i.e., 1 and
0. Thus, its base is 2.
Binary Number is represented as (1000111)2.
The Decimal number System uses 10(Decimal) numerals i.e.,
0,1,2,3,4,5,6,7,8 and 9 . Thus , the base of this number system
is 10.
Decimal Number is represented as (235427)10.
6. This number system uses total 16 different symbols i.e., 0,1,2,
3,4,5,6,7,8,9,A,B,C,D,E and F. The symbols from A-F represents
values from ten to fifteen. Thus, its base is 16(hex).
Hexadecimal number is represented as (21AC2)16.
In this system, 8 different symbols are used i.e., 0,1,2,3,4,5,6
and 7. Thus, its base is 8(octal).
Octal number is represented as (3175)8.
9. Technique
Multiply each bit by 2n, where n is the “weight” of the
bit
The weight is the position of the bit, starting from 0
on the right
Add the results
10. 1010112 => 1 x 20 = 1
1 x 21 = 2
0 x 22 = 0
1 x 23 = 8
0 x 24 = 0
1 x 25 = 32
4310
Bit “0”
12. Technique
Multiply each bit by 8n, where n is the “weight” of
the bit
The weight is the position of the bit, starting from 0
on the right
Add the results
13. 7248 => 4 x 80 = 4
2 x 81 = 16
7 x 82 = 448
46810
15. Technique
Multiply each bit by 16n, where n is the “weight” of
the bit
The weight is the position of the bit, starting from 0
on the right
Add the results
16. ABC16 => C x 160 = 12 x 1 = 12
B x 161 = 11 x 16 = 176
A x 162 = 10 x 256 = 2560
274810
18. Technique
Divide by two, keep track of the remainder
First remainder is bit 0 (LSB, least-significant bit)
Second remainder is bit 1
Etc.
56. Binary Coded Decimal
Introduction:
Although binary data is the most efficient storage scheme; every bit pattern
represents a unique, valid value. However, some applications may not be
desirable to work with binary data.
For instance, the internal components of digital clocks keep track of the
time in binary. The binary value must be converted to decimal before it
can be displayed.
57. Binary Coded Decimal
Because a digital clock is preferable to store the value as a
series of decimal digits, where each digit is separately
represented as its binary equivalent, the most common
format used to represent decimal data is called binary
coded decimal, or BCD.
62. Algorithms for Addition
Two errors will occurs in a standard binary adder.
(1 ) The result is not a valid BCD digit.
(2) A valid BCD digit, but not the correct result.
Solution: You need to add 6 to the result generated by a binary adder.
63. Algorithms for Addition
A simple example of addition in BCD.
0101
+ 1001
1110
+ 0110
1 0100
5
+ 9
Incorrect BCD digit
Add 6
Correct answer
1 4
64.
65. Logic gates perform a logic operation on one or
more logic inputs and produce a single logic
Output.
Basic Types of Logic Gates or Universal Gates
AND Gate,
OR Gate and
NOT Gate
