Digital Representation.

             Digital representation

ASCII(American Standing Code for Information Interchange)

• It is 7 bits code.
• Total 127 different characters are represented by ASCII code.
• It starts from 0 to 126.
• The ASCII code is a subset of UTF-8 code.
• Unicode characters code is a superset of ASCII .

 Types of Number system

1. Binary (2 bases)

• symbol:{0,1}

1. Decimal(10 bases)

• symbol:{0,1,2,3,4,5,6,7,8,9}

1. Hexadecimal(16 bases)

• symbol:{0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}

1. Octal(8 bases)

• symbol:{0,1,2,3,4,5,6,7}

Number representation - signed

• positive values have same representation. 
• Negative numbers have different representation.

Three ways to signed integer:

1. Sign and magnitude
2. 1's complement
3. 2's complement

Rules for adding the binary number.

1. 0 + 0 = 0
2. 1 + 0 = 1
3. 1 + 1 = 10(2 binary)
4. 1 + 1+ 1 = 11(binary)

Rules for subtracting the binary number.

1. 0 - 0 = 0
2. 1 - 1 = 1
3. 1 - 1 = 0
4. 0 - 1 = 1(borrow 1)

• when we subtract 1 from 0, we have to borrow 1 next high digit.

• Overflow occurs when the magnitude of a number exceeds the range allowed by the size of the bit field.

When adding overflow occurs  if :

• (+A) + (+B) = -C
• (-A) + (-B) = +C

when subtracting overflow occurs if:

• (+A) - (-B) = -C
• (-A) - (+B) = +C

For signed integer, the leftmost bit is used to indicate the signs:

• 0 for positive 
• 1 for negative 
• Rang: -2^(n-1) to +2^(n-1) - 1
• 4 bits: -8 to 7(2^3 to 2^(3)-1)