Systems and Networks
COMPSCI 4043
December 2022
1. (a) Express the following in 16-bit two’s complement representation, giving your answers in hexadecimal. Show your working.
i. 1000 ii. -2000 [4]
(b) Recall that a sign-and-magnitude code represents integer values by using the most significant bit to indicate the sign, and the remaining bits to hold the magnitude (or size) of the number. Thus $8002 is -2, while $0002 is +2, and soon.
Write a commented Sigma16 program to convert a variable, x, containing a 16-bit integer value in sign-and-magnitude form, into to a two’s complement value stored in another variable y. Thus $8001 (sign and magnitude code for -1) should turn into $FFFF (two’s complement code for -1) and soon. Assume that x will never contain the anomalous sign-and-magnitude code for “negative zero” ($1000) so you do not need to check for this. [5]
(c) Write a Sigma16 program to read a 16-bit variable x, swap the most significant and least
significant bytes and store the result in another variable y. Thus, if x contains $1234 initially, y should be $3412 etc. [4]
(d) Write a commented Sigma16 program to process an array, X, of n 16-bit signed numbers in memory. If a number is positive, double it; if it is negative, square it (multiply it by itself). [7]
For reference, here is a summary of the instruction set of the Sigma16 CPU.
Mnemonic Syntax Action
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lea
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Rd, x[Ra]
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Rd:= x +Ra
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load
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Rd, x[Ra]
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Rd:= mem[x +Ra]
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store
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Rd, x[Ra]
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mem[x +Ra]:=Rd
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add
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Rd,Ra,Rb
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Rd:= Ra+Rb
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sub
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Rd,Ra,Rb
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Rd:= Ra-Rb
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mul
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Rd,Ra,Rb
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Rd:= Ra*Rb
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div
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Rd,Ra,Rb
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Rd:= Ra/Rb, R15:=Ra mod Rb
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and
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Rd,Ra,Rb
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Rd:= Ra AND Rb
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inv
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Rd,Ra,Rb
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Rd:= NOT Ra
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or
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Rd,Ra,Rb
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Rd:= Ra OR Rb
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xor
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Rd,Ra,Rb
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Rd:= Ra XOR Rb
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cmplt
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Rd,Ra,Rb
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Rd:= Ra<Rb
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cmpeq
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Rd,Ra,Rb
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Rd:= Ra=Rb
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cmpgt
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Rd,Ra,Rb
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Rd:= Ra>Rb
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shiftl
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Rd,Ra,Rb
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Rd:=Ra logic shifted left Rb places
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shiftr
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Rd,Ra,Rb
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Rd:=Ra logic shifted right Rb places
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jumpf
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Rd, x[Ra]
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If Rd=0 then PC:=x+Ra
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jumpt
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Rd, x[Ra]
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If Rd<>0 then PC:=x+Ra
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jal
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Rd, x[Ra]
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Rd:= pc, pc: =x +Ra
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trap
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Rd,Ra,Rb
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PC:= interrupt handler
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jump
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x[Ra]
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PC:= x +Ra
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2 (a) Taking the Sigma16 instruction STORE R4, 100[R1] as an example, describe how this would appear as
machine code in memory and outline the steps involved in fetching and executing it. [6]
(b) The following Sigma16 code is intended to take a 10-element array of two’scomplement numbers (only the first DATA element is shown), replace every odd element with 1 and every even element with 0.
However, although the code will assemble, it contains several logical errors (as opposed to syntax errors or inefficiencies, which you may ignore).
i. Draw up a register use table for the program (suitable for inclusion as comment).
ii. Identify the errors and explain how you would correct them.
iii. Write out the corrected program.
LEA R1,1[R0] ;Set R1 to constant 1
LOAD R2,0[R0] ;i:=0
ADD R5,R1,R1 ;R5:=2
LOAD R3,n[R0] ;Set R3 to n
FOR CMPEQ R14,R3,R2 ;Is i=n?
JUMPF R14,OUT[R0] ;if yes, exit
LOAD R4,X[R2] ;load X[i]
DIV R6,R4,R5 ;R6= X[i] mod 2
ADD R2,R2,R1 ;i:=i+1
STORE R6,X[R2] ;X[i]=X[i] mod 2
JUMP FOR[R0] ;loop
OUT TRAP R0,R0,R0 ; Data Area
n DATA 10
X DATA -8
DATA ... [6]
(c) Estimate how many memory cycles the corrected program would take to run. [4]
(d) In the corrected program estimate the advantage a system with a cache memory would gain if a primary memory cycle took 10ns and a cache cycle 1ns. [4]
3. (a) Processors that support multitasking operating systems (unlike Sigma16) will generally have
privileged instructions in their instruction sets. Explain why the notion of “privilege” is necessary and give two examples of what such instructions might do. [5]
(b) Explain why analogue transmission of data is more vulnerable to noise than digital. If bit errors do occur in digital transmission, briefly describe one way these might be detected. [5]
(c) UDP is often used to transmit real-time audio (e.g. in VoIP applications). Explain why UDP might be considered more suitable than TCP for this purpose. [5]
(d) Suppose a TCP sender is transmitting at 1.5Gbytes/sec (1.5 x 109 bytes/sec) with TCP segments that
are approximately 1500 bytes long. Each segment has a 32-bit (unsigned) sequence number in its header that is incremented by 1 at the sender each time a new segment is transmitted. If the first segment sent has number 0, how long before the numbers run out? Discuss briefly what would happen then? [5]