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DRAM capacity 1000M ~2004 1000 512M 256M 100 Mbit capacity 64M 10 16M 1M 1 64K 0.1 4M 256K 15K 0.01 0.001 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 Hardware Computer Organization for the Software Professional Arnold S. Berger 1998 2000 1 Abstract view of a computer Hardware Computer Organization for the Software Professional Arnold S. Berger 2 Abstraction layers Hardware Computer Organization for the Software Professional Arnold S. Berger 3 Memory hierarchy • • • There is a hierarchy of memory In order to maximize processor throughput, the fastest memory is closest to the processor Primary Cache - Also the most expensive CPU 2K- 1,024K byte (<1ns) Notice: - The exponential rise in capacity Bus Interface Unit with each layer - The exponential rise in access time Secondary Cache 256K - 4MByte (10ns) in each layer Main Memory 1M – 2 Gbyte (30 ns) Hard Disk 40 - 250 GByte ( 100,000 ) ns Tape Backup 50G - 10TByte (seconds) Internet All knowledge/Forever Hardware Computer Organization for the Software Professional Arnold S. Berger 4 Hard disk drive Hardware Computer Organization for the Software Professional Arnold S. Berger 5 Representing a number as a voltage • Represent the data value as a voltage or current along a single electrical conductor (signal trace) or wire 24.56345 RADIO SHACK 24.56345 V Direction of signal • Problems: • Measuring large numbers is difficult, slow and expensive • How do you represent +/- 32,673,102,093? Hardware Computer Organization for the Software Professional Arnold S. Berger Zero volts (ground) 6 Parallel transmission of 0 to 9 • Represent the data value as a voltage or current along multiple electrical conductors •Let each wire represent one decade of the number • Only need to divide up the voltage on each wire into 10 steps • 0 V to 9 volts • Can have considerable “slop” between values before it causes problems 4.2 RADIO SHACK 2 4 5 6 3 4 5 Zero volts (ground) Hardware Computer Organization for the Software Professional Arnold S. Berger 7 Binary data transmission • Represent the data value as a voltage or current along multiple, parallel, electrical conductors •Let each wire represent one power of 2 of the number ( 20 through 2N ) • Only need to divide up the voltage on each wire into 2 possible steps • 0 V “no volts” or “some volts” greater than zero (on or off ) • Can have lots of “slop” between values 20 21 22 23 24 25 26 27 28 29 210 211 212 213 214 215 Hardware Computer Organization for the Software Professional Arnold S. Berger on off on off off on on on off off off on on on on off 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 8 A simple AND circuit • • • Digital computers force us to deal with number systems other than decimal - ALL digital computers are collections of switches made from transistors - A switch is ON or OFF - A binary (digital) system lends itself to using electronic on/off switching Principles of Logic (a branch of Philosophy ) are useful to describe the digital circuits in computers - True/False, 1/0, On/OFF, High/Low all describe the same possible states of a digital system An electrical circuit, with ordinary switches, is a convenient display on/off switch A + B C C = A and B Battery Symbol - Light bulb (load) Hardware Computer Organization for the Software Professional Arnold S. Berger 9 Decimal representation • • • • Writing a number is the same in all number systems Each column of the number represents the base that the number is raised to Example: 65,53610 = 216 104 103 102 101 100 6 5 5 3 6 Notice how each column is weighted by the value of the base raised to the power + 6 x 100 = 6 3 x 101 = 30 5 x 102 = 500 5 x 103 = 5000 6 x 104 = 60000 = 65536 Hardware Computer Organization for the Software Professional Arnold S. Berger 10 Binary numbers • • Just like decimal numbers, binary numbers are represented as the power of the base: Example: 10101100 Bases of Hex and Octal B 1 0 1 0 1 1 0 0 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 = 128 = 0 = 32 = 0 = 8 = 4 = 0 = 0 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 1 0 1 0 1 1 0 0 10101100 2 = 172 10 172 Hardware Computer Organization for the Software Professional Arnold S. Berger 11 Binary and octal numbers • • Let’s look at our example again: Notice that because 8 = 23 we can easily convert binary to octal - Just group columns of three and treat as binary within a column to get octal number from 0 to 7 82 81 80 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 26 (21 1 20 ) 0 0 thru 192 23( 22 1 21 0 0 thru 56 20) 1 20 ( 22 1 21 0 4 x 80 = 4 5 x 81 = 40 2 x 82 = 128 172 20) 0 0 thru 7 Hardware Computer Organization for the Software Professional Arnold S. Berger 12 Binary and hex • • Hexadecimal is the same principle as octal - Hexadecimal is the most common number system in computer science - Octal was common with minicomputers but is now a special function counting system Back to our example: 10 x 16 + 12 x 1 = 172 = AC (Hex) 161 128 64 160 32 16 8 4 2 1 22 21 20 27 26 25 24 23 24(23 22 21 20) 20 ( 23 1 0 1 0 1 22 21 20) 1 0 0 Hardware Computer Organization for the Software Professional Arnold S. Berger 13 Bits, bytes, nibbles, words, etc. Bit (1) D3 D0 Nibble (4) D7 D0 Byte (8) D15 D31 D0 Word (16) D0 Long (32) D63 D0 Double (64) D127 D0 VLIW (128) Hardware Computer Organization for the Software Professional Arnold S. Berger 14 A Seven Segment Display using BCD 0000 0001 0010 0011 0101 0100 carry the one 0110 0111 1000 1001 0001 Hardware Computer Organization for the Software Professional Arnold S. Berger 0000 15