Page 18 - DCAP104_EXPOSURE_TO_COMPUTER_DISCPLINES

Unit 1: Data Information

Notes
Arithmetic addition Arithmetic Subtraction
Arithmetic addition: Complexity Arithmetic Subtraction: The sub-
of arithmetic addition is dependent traction can be easily done using
on the representation the 2’s complement by taking the
2’s complenient of the subtractend
(inclusive of sign bit) and then adding
the two numbers.

1.2.5 Decimal Fixed Point Representation

A decimal digit is represented as a combination of four bits; thus, a four digit decimal number
will require 16 bits for decimal digits representation and additional 1 bit for sign. Normally to
keep the convention of one decimal digit to 4 bits, the sign sometimes is also assigned a 4-bit code.
This code can be the bit combination which has not been used to represent decimal digit e.g., 11
00 may represent plus and 1 101 can represent minus.
Although this scheme wastes considerable amount of storage space yet it do not require conversion
of a decimal number to binary. Thus, can be used at places where the amount of computer
arithmetic is less than the amount of input output of data e.g. calculators or business data
processing. The arithmetic in decimal can also be performed as in binary except that instead of
signed one’s complement, signed nine’s complement is used and instead of signed 2’s complement
signed 10’s complement is used.
1.2.6 Floating Point Representation

Floating-point number representation consists of two parts. The first part of the number
is a signed fixed point number. which is termed as mantissa. and the second part specifies
the decimal or binary point position and is termed as an Exponent. The mantissa can be an
integer or a fraction. Please note that the position of decimal or binary point is assumed
and it is not a physical point, therefore, wherever we are representing a point it is only
the assumed position.

A decimal +12.34 in a typical floating point notation is:

Solution

sign sign

0 1234 0 02
Mantissa (fraction) Exponent

sign sign

0 1234 0 02
Mantissa (integer) Exponent

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