Bits, Data types, and Operations: Chapter 2 COMP 2610 Dr. James Money COMP

Floating Point Data Type Most ISAs have a data type called float, which is 32 bits arranged as follows – 1 bit for sign – 8 bits for range of exponent – 23 bits for the precision or fraction This is called the IEEE Standard for Floating Point Arithmetic

Floating Point Data Type

Recall the bits in the fractional part are of the form 1.b -1 b -2 …b -j The corresponding decimal number is 1x2 0 + b -1 x2 -1 +b -2 x2 -2 +… + b -j 2 -j

Floating Point Data Type If the exponent= , then we can represent tiny numbers. In this case, we assume the leading digit is zero and not 1 and exp=-126. That is, it is of the form -1 s 0.fraction x

Floating Point Data Type Consider the floating point value This is x =

Floating Point Data Type Interpret the floating point values – – –

ASCII Codes Another standard of representation is one for transferring character codes This is an eight bit code referred to ASCII ASCII stands for American Standard Code for Information Exchange It simplifies the interface between I/O devices among companies

ASCII Codes Each key on a keyboard is identified by a unique ASCII code The digit 3 is ( ) 2 = (41) 10, digit 3 is ( ) 2 = (40) 10 The letter ‘e’ is ( ) 2 and carriage return is ( ) 2

ASCII Codes The list of codes are at the back of the book for all 256 ASCII codes Some codes are associate with multiple keys, such as ‘e’ and ‘E’

Hexadecimal Notation One form that is common for reading values on the computer is called hexadecimal notation Hexadecimal notation is the base 16 representation of the number

Hexadecimal Notation We use 0-9 for the same numbers in hexadecimal What about 10-15? We use the letters A-F

Hexadecimal Notation A – 10 B – 11 C – 12 D – 13 E – 14 F - 15

Hexadecimal Notation Consider the binary string This can be broken into groups of 4 bits: Now, recall that the range of 4 bits is 0 -15, just like hexadecimal notation

Hexadecimal Notation Hence, the numbers represent We typically prefix this by x or 0x to indicate hexadecimal form So our binary number is 0x3D6E D6E

Hexadecimal Notation What is the number 0x5A6C in binary form? Thus, (5A6C) 16 = ( ) 2 5A6C