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L02-notes

# L02-notes - Computer Architecture Margot Gerritsen Shela...

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Computer Architecture Margot Gerritsen Shela Aboud Emmet Caulfield January 5, 2010 1

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Outline Outline Computers represent everything in binary , so we’ll review number systems before we talk about computer architecture. Contents 1 Number Systems and Representations 1 1.1 Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Machine Architecture 4 There are many different kinds of computer systems from largely invisible em- bedded systems in microwave ovens and cars, through devices we don’t usually think of as computers per se , but would immediately know are (to a large degree at least), like iPods and cellphones, to the “real” (general-purpose) computers like servers, desktops, and notebooks that we think of as “computers” proper. For our current purpose, we adopt a fairly narrow meaning of “computer” to mean a computer like a Mac or a PC. But before we can understand the basic architecture of the computer, we have to have a little background information about how computers represent data. As you probably already know, computers store information in “ones and zeros” — in binary . 1 Number Systems and Representations You probably know that computers are essentially devices that manipulate num- bers extremely quickly and have heard of computers being “32-bit” or “64-bit”, which is the number of bits — binary digits — in the microprocessor’s registers (a kind of scratchpad within the microprocessor where a number can be manip- ulated). Historically, the first microprocessor (the Intel 4004) was 4-bit, later microprocessors were 8-bit, 16-bit, and 32-bit. Modern processors are 32-bit or 64-bit, but even now 8-bit microprocessors are still used in embedded systems like dishwashers and microwave ovens. 1.1 Bases In binary, the weights of positions, rather than being units, tens, hundreds,
Number Systems & Computer Architecture Outline Number Systems and Representa- tions Bases Representations Machine Architecture Number Systems & Representations Number systems — base- n , binary, octal, hexadecimal Representation of integer, negative, and fractional numbers Motivate the notion of type Figure 1: Number Systems and Representations thousands, . . . , are instead units, twos, fours, eights, sixteens, etc. It should be obvious that any integer that can be represented in one number system can be represented in another. For real numbers, the only difference is that numbers that recur after the decimal point typically don’t in other number systems – consider 1 3 in bases 10 and 3 — (0 . 333 . . . 10 = 0 . 1 3 ). In a computer, the number of values that can be represented in a memory region or a register is dependent on the number of bits — in a nybble (4 bits) 16 distinct values can be represented; in a byte (8 bits), 256; in 16 bits (two bytes), 65536, etc. 1.2 Representations We need to be able to represent negative numbers and fractional numbers in binary too, so the question arises, how is that done?

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