Bits, Nibble, Bytes, and Word

Associative
A + (B + C) = ( A + B) + C
A. (B. C) = (A . B) .C

The truth table for XOR gate is

(28)₁₀ is a positive number. 1's complement represent signed numbers (Negative numbers) only. So, (28)₁₀ cannot find 1's complement.

Step 1: Convert given Decimal number into Binary
Step 2: Check if the binary number contains 8 bits. if less add 0 at the left most bit, to make it as 8 bits.
Step 3: Invert all bits (i.e. Change 1 as 0 and 0 as 1).

De Morgan's
\(\bar { A+B } =\bar { A } .\bar { B } \)
\(\left( \bar { A.B } \right) =\bar { A } +\bar { B } \)

NAND and NOR gates are called Universal gates, because the fundamental logic gates can be realized through them

a) AND gate truth table

b) OR Gate Truth table

c) Not Gate Truth Table

(i) ISCII is the system of handling the character of Indian local languages. This as a 8-bit coding system.
(ii) Therefore it can handle 256 (28) characters. This system is formulated by the department of Electronics in India in the year 1986-88 and recognized by Bureau of Indian Standards (BIS).
(iii) Now this coding system is integrated with Unicode.

(i) There are only two digits in the Binary system, namely, 0 and 1.
The numbers in the binary system are represented to the base 2 and the positional multipliers are the powers of 2.
(ii) The left most bit in the binary number is called as the Most Significant Bit (MSB) and it has the largest positional weight.
(iii) The right most bit is the Least Significant Bit (LSB) and has the smallest positional weight.

645₈
\(\overset { 6 }{ \underset { 110 }{ \downarrow } } \) \(\overset { 4 }{ \underset { 100 }{ \downarrow } } \) \(\overset { 5 }{ \underset { 101 }{ \downarrow } } \)
645₈ = 110100101₂

(A) - 22

Binary equivalent of + 22  =10110
8 bit format                            =00010110
1's complement                    =11101001
Add 1 to LSB                          =            +1
2's complement of -22     =\(\_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 11101010\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \)   
(B) -13
  
Binary equivalent of + 13 =1101
8 bit format                       =00001101
1's complement                =11110010
Add 1 to LSB                    =            +1
2's complement of-13         \(\_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 11110011\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \)
(C)-65

Binary equivalent of + 65  =1000001
8 bit fomiat                        =01000001
1's complement                 =10111111
Add 1 to LSB                     =           +1
2's complement of -65       =\(\_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 11000000\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \)
(D)-46

Binary equivalent of + 46  =101111
8 bit format                        =00101111
1's complement                  =11010000
Add 1 to LSB                        =           +1
2's complement of-46           \(\_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 11010001\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \)
(E)-255

Binary equivalent of + 255    =11111111
1's complement                     =00000000
Add 1 to LSB                         =            +1
2's complement of - 255        = \(\_ \_ \_ \_ \_ \_ \_ \_ \\ 00000001\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \)

ISCII (Indian Script Code for Information Interchange):
(i) In order to encode Indian languages Ion computers, a common standard for coding Indian scripts is developed which is called as ISCI!. In 1991, the Bureau of Indian Standards adopted the Indian Standard Code for Information Interchange (ISCII).
(ii) ISCII standard is evolved by a standardization committee during 1986-88. The ISCII document is available as IS 13194: 1991 from the BIS offices.
(iii) Assamese, Bengali (Bangla), Devanagari, Gujarati, Gurumukhi, Kannada, Malayalam, Oriya, Tamil, and Telugu are supported in ISCII. ISCII has been used by IBM for PCDOS, Apple for ILK, and several companies are developing products and solutions based on this representation.
TSCII (Tamil Standard Code for Information Interchange):
(i) Tamil Standard Code for Information Interchange is the Tamil encoding scheme designed to handle the entire Tamil alphabet. TSCII is proposed by the Internet Working Group for the Tamil Standard Code (IWG-TSC).
(ii) The Tamil alphabets have soup (247), grantha characters (13), and Tamil numerals (13). The number of unique Tamil glyphs to consider is about 170. Since the number of slots available in the upper-ASCII segment (#128-255) is much less than the required slot for each character in Tamil.
(iii) Therefore, few Tamil alphabets are to be included in the native form, and the others are generated using modifiers (several keystrokes in sequence).

a) -98

= 98₁₀ = 1100010
8bit format of 98₁₀ =     0 1 1 0 0 0 1 0
1's complement    =     1 0 0 1 1 1 0 1
Add 1 Bit                =                       +1
                                    _____________
2's complement           1 0 0 1 1 1 1  0
                                    _____________
b) -135

= 135₁₀ = 10000111
1's complement  =      0 1 1 1 1 0 0 0
Add 1 bit             =                     +  1
                                 ______________
2's complement  =       0 1 1 1 1 0 01
                                _______________