Computer Organization Computer Architecture Floating point formats

1. Introduction
Dhaval Bagal

2. • Architecture is those attributes visible to the programmer The attributes that have
direct impact on the logical execution of a program
• Examples of architectural attributes are
Instruction set, number of bits used for data representation, I/O mechanisms,
addressing techniques.
• Architectural design issue
e.g. Is there a multiply instruction?
• It focuses on what to do?
• It deals with high level issues
Computer Architecture

3. • Computer Organization refers to the operational units and their interconnections that
realize the architectural specifications
• Organizational attributes include - Control signals, interfaces, memory technology.
• Organizational issue - E.g. Is there a hardware multiply unit or is it done by repeated
addition? ( decision—speed, cost, physical size)
• It focuses on how to do?
• It deals with low level issues
• The architecture may not change for many years but the organization changes with the
change of technology. This means that the same software can be used on different
models of the computer, only the hardware changes to make the system improve in
performance and speed.
Computer Organization

4. • We can represent a number in the form
+- S X B+-E
This number can be stored in a binary word with three fields:
• Sign: plus or minus
• Significand S
• Exponent E
Floating point formats

5. • The leftmost bit stores the sign of the number (0 = positive, 1 = negative).
• The exponent value is stored in the next 8 bits.
• The representation used is known as a biased representation.
• A fixed value, called the bias, is subtracted from the field to get the true exponent
value. Typically, the bias equals (2k - 1 - 1), where k is the number of bits in the binary
exponent.

6. • To simplify operations on floating-point numbers, it is typically required that they be
normalized.
• A normal number is one in which the most significant digit of the significand is
nonzero.
• For base 2 representation, a normal number is therefore one in which the most
significant bit of the significand is one.
• Thus, a normal nonzero number is one in the form
1.bbb…b x 2+-E
• where b is either binary digit (0 or 1). Because the most significant bit is always one, it
is unnecessary to store this bit; rather, it is implicit.

7. • The biased exponent is used to store negative exponents.
• It has advantages over 2s compliment representation in performing bitwise
comparison of 2 floating point numbers for equality.
• E.g
(22.75)10
(10110.11)2
1.011011 x 24
E = e + 127 (28-1 - 1 = 127)
= (131)10
= (10000011)2
0 10000011 011011 00000000000000000