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CS/COE0447

Computer Organization & Assembly Language

Pre-Chapter 2

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“C Program” Down to “Numbers”

swap:muli $2, $5, 4add $2, $4, $2lw $15, 0($2)lw $16, 4($2)sw $16, 0($2)sw $15, 4($2)jr $31

void swap(int v[], int k){

int temp;temp = v[k];v[k] = v[k+1];v[k+1] = temp;

}

00000000101000010…00000000000110000…10001100011000100…10001100111100100…10101100111100100…10101100011000100…00000011111000000…

compiler

assemble

r

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“Numbers” in Memory

00000000101000010…00000000000110000…10001100011000100…10001100111100100…10101100111100100…10101100011000100…00000011111000000…

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Stored Program Concept

processor

main memoryhard disk

program A

program Bprogram C

program A

program B

data A

data B

program fetchdata load/store

disk I/Oprogramcounter

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Stored Program Concept

• Programs (instructions) are stored in memory as a stream of bits (numbers)– Indistinguishable from data– More than one program can reside in memory at

the same time– Programs can be modified by the processor or I/O

just as data can be modified• Instructions are fetched by the processor and

decoded; they determine processor actions• Program Counter determines which instruction is

fetched next

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Stored Program Concept

• In fact, one of the great ideas in computer science is the idea that programs could be stored just as data is stored.

• Before that, people envisioned the hardware running a fixed program, and data being stored in memory.

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…

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10

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Addresses and Contents shown in Hex

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Number Systems

• Actual machine code is in binary – O, 1 are high and low signals to hardware

• Hex (base 16) is often used by humans (code, simulator, manuals, …) because:

• 16 is a power of 2 (while 10 is not); mapping between hex and binary is easy

• It’s more compact than binary• We can write, e.g., 0x90000008 in programs rather

than 10010000000000000000000000001000

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Base 10 (Decimal)

• Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (10 of them)

• Example:– 3217 = (3103) + (2102) + (1101) + (7100)– A shorthand form we’ll also use:

103 102 101 100

3 2 1 7

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Numbers and Bases in General

• Number Base B B unique values per digit– Base 10: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}– Base 2: {0, 1}– Base 16: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}

• (Unsigned) number representation

– d31d30…d1d0 is a 32-digit non-negative number

– Value = d31B31 + d30B30 + … + d1B1 + d0B0

• N-digit base B BN unique values in N digits of base B

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Example: Base 2 (Binary)

• Digits: 0, 1 (2 of them)• “Binary digit” = “Bit”

• Example:

– 11010two = (124) + (123) + (022) + (121) + (020) = 16 + 8 + 0 + 2 + 0 = 26ten

• Choice for machine implementation!– 1 = on, 0 = off

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Base Conversion

• Let’s do decimal-to-binary conversion:

• Aten = dn-1dn-2…d1d0two

• Given a base-10 number A, come up with n-digit binary number that has the same value!– X = the number– Let N be the largest power of 2 that fits into X– Put a 1 in that position– X = X – 2^N– Repeat until you are done!

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Base Conversion, cont’d

• From binary to decimal

• From decimal to binary

• From binary to hexadecimal

• From hexadecimal to binary

• From decimal to hexadecimal? (more complicated; later)

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Base Conversion, cont’d

• Binary to hex (base 16), or hex to binary base conversion:– Take 4 bits in binary and convert them into one hex digit

and vice versa– For binary hex: 4-bit groups, starting from the right– For hex binary: translate each hex digit into 4 bits,

starting from the right

• Since binary notation tends to be long, hex notation is frequently used in assembly language (and in C programs).

• More on binary number representation will be discussed when we study arithmetic

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Before moving on to chapter 2….

• We’ll mention some concepts in program performance, so you have ideas in mind

• We’ll return to this material later in the course.

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Program Performance

• Program performance is measured in terms of time!

• Program execution time depends on:• Number of instructions executed to complete a job• How many clock cycles are needed to execute a

single instruction• The length of the clock cycle (clock cycle time)

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Clock, Clock Cycle Time

• Circuits in computers are “clocked”• At each clock rising (or falling) edge, some specified actions

are done, usually within the next rising (or falling) edge• Instructions typically require more than one cycle to execute

Function block(made of circuits)

clock

clock cycle time

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Program Performance

• time = (# of clock cycles) (clock cycle time)

• # of clock cycles =

(# of instructions executed)

(average cycles per instruction)

• We’ll do specific calculations later

• But now, let’s move on to Chapter 2