CS 2011 Introduction of Computer System Lecture 2 (Week 3 notes)
CS 2011 Introduction of Computer System Lecture 2 (Week 3 notes) CS2011
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This 2 page Class Notes was uploaded by Nemesi Notetaker on Thursday January 28, 2016. The Class Notes belongs to CS2011 at University of Cincinnati taught by Dr.Eric Hozier in Spring 2016. Since its upload, it has received 35 views. For similar materials see Introduction to Computer Systems in Computer Science and Engineering at University of Cincinnati.
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Date Created: 01/28/16
Module2 How can we represent numbers in a computer? Numbers are kept in computer hardware as a series of high and low electronic signals, By encoding the signal we obtain values are above or below some threshold of pulses, we represents them as 1 3.3V2.8V (T), or a 0 (F) 0.5V0V. Strings of 1’s and 0’s can be interpreted as a number. all information are composed of binary digits or bits Also called binary bit. computer use on and off signals, so a decimal digit was simply represented by several binary digits. Decimal proved so inefficient. Conversion Formula • Given an nbit number x x 2 n1 x 2n2 x 2 x 2 0 n1 n2 1 0 Ex: 0000 0000 0000 0000 0000 0000 0000 1011 2 = 0 + … + 1×2 + 0×2 +1×2 +1×2 0 = 0 + … + 8 + 0 + 2 + 1 = 110 Placing these binary numbers side by side forms the instruction. Representing Instructions in the Computer you can see from counting the number of bits, this MIPS instruction takes exactly 32 bits—the same size as a data word. it from assembly language, we call the numeric version of instructions machine language and a sequence of such instructions machine code. Since almost all computer data sizes are multiples of 4, hexadecimal (base 16) numbers are popular. Since base 16 is a power of 2, we can trivially convert by replacing each group of four binary digits by a single hexadecimal digit, and vice versa Conversion Formula 0 0000 4 0100 8 1000 c 1100 1 0001 5 0101 9 1001 d 1101 2 0010 6 0110 A 1010 e 1110 3 0011 7 0111 B 1011 f 1111 Example: eca8 6420 will result in: 1110 1100 1010 1000 0110 0100 0010 0000 ( where every 4 bits is per hex digit) Limits of every digit languages = Every language analyzed has limits so if the value will be outrangeof those in will result in the max value possible (ex. Dec 259 will be 255) Hex:00 16o FF 16 Dec: 010to 25510 Bin:00000000 2o 11111111 2 Numbers ver this value will not be rappresentabile In computer science, Languages are connected to Alan Turing's work on algorithms, computability and to compiler design thanks to a set of rules called Chomsky’s Hierarchy. Chomsky’s Hierarchy= It is a containment hierarchy of classes of formal grammars (a set of production rules for strings in a formal language) The Chomsky hierarchy consists of the following levels, each of is a subset of the classes above it, : *wiky Date representation= Instruction are plugged as a Most current machines use 32 bits (4 bytes) words and the Limits addresses to 4GB Byte Ordering= depending on the processor Text representation of binary machine code are readed in a different way. Endianess, describes the order of byte transmission over a digital link. Big Endian: Sun, PPC Mac, Internet Least significant byte has highest address Little Endian: x86 Least significant byte has lowest address EX Variable x has 4byte representation 0x01234567 01 23 45 67 Example Fragment • Deciphering Numbers • Value: 0x12ab • Pad to 32 bits: 0x000012ab • Split into bytes: 00 00 12 ab • Reverse: ab 12 00 00
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