2. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/1/21 COM347J1 Networks and Data Communications Ian McCrumRoom 5D03B Tel: 90 366364 voice mail on 6 th ring Email: IJ.McCrum@Ulster.ac.uk Web site: http://www.eej.ulst.ac.uk Sums Lecture (and Tuts on ohp 15, 17 & 19)

3. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/2/21 Binary and Hex Hex is just a shorthand way of writing binary Binary is always written with b0 on the right Hex always considers the binary is split into groups of 4, starting at the right For each group of 4 binary bits, use the table to look up what single character to write down in place of the 4 bits E.g 01001001 is [0100][1001] is ‘4’ ‘9’ E.g 101110 is [oo10][1110] is ‘2’ ‘E’ Unfortunately data is transmitted bit zero first, usually drawn with bit zero on left if drawing square waves, also RS232 uses –12V for ‘1’, +12v for ‘0’ We could use “base-2” or “base-16” arithmetic, let the 4 bits have weights 8421 [0000] = ‘0’ [0001] = ‘1’ [0010] = ‘2’ [0011] = ‘3’ [0100] = ‘4’ [0101] = ‘5’ [0110] = ‘6’ [0111] = ‘7’ [1000] = ‘8’ [1001] = ‘9’ [1010] = ‘A’ [1011] = ‘B’ [1100] = ‘C’ [1101] = ‘D’ [1110] = ‘E’ [1111] = ‘F’ So ‘A’ = 1010, 8+2 =10, one more than 9…

4. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/3/21 Basics or

5. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/4/21 Description In English we would say 2 to the power of 3 is 8. In other words 2 must be multiplied by itself 3 times in order that the answer 8 is achieved. What is 2 10 equal to? The answer is 1024 come on do it

6. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/5/21 More Whenever you wish to work in reverse you use a different way of describing the problem. One might say “to what power must I raise 2 to in order to produce the number 32?” And of course the answer is 5 Another way of expressing that is by saying “what is the log of 32?” (really should say log to the base 2, or mathematically log 2 )

7. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/6/21 Mathematicians write that in the following way

8. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/7/21 But what if you are asked the following question What is Log 2 1000? - you know that it is less than 10 because Log 2 1024 is equal to 10 but what is the exact value? Here is a useful formula which shows you how to do it - What that means in practice is - consider the log button on your calculator, it works to some base usually 10 but it could have other values

9. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/8/21 You just take the log of the number you want the log 2 (log to the base two) of, and divide it by the log of the number 2. Look at the formula again The x is the value 2 and the z is the base to which your calculator works (normally 10) so

10. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/9/21 So we were right, the answer is just less than 10 If your calculator has a ln button that is log to the base e where e=2.718 you can try it and you will get the same answer look!

11. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/10/21 When ever people have very big numbers or very small numbers, they might choose a different way to present them. This is also true if they have some property they wish to highlight One such case is power ratios in electronic circuits. A person might wish to describe the ratio as 1 : 100 or 1 : 1000000 or 1 : 100000000, you like me, might find it difficult to decide what the actual ratio was when it is so written.

12. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/11/21 Now that you know about logs you might describe the ratios on the previous slide in terms of log to the base 10. 1 : 100 as 2 and 1 : 1000000 as 6 and 1 : 100000000 as 8 Now isn’t that more tidy and it also make you concentrate upon the important thing about the number, its magnitude, not its precise value(these are Bells). - there’s more

13. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/12/21 However this can go too far and because of the nature of the value that we use the range would be limited from 1.0 to 9.0 and we would need to include the decimal point to give the required accuracy to our calculations. So we go one step further. We multiply the log of the ratio by 10 and leave out the decimal point. And we call them deciBells ie 1/10th part of a Bell. (dB)

14. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/13/21 So if you wish to find out the precise value of a ratio which is expressed in dB for example 40 dB Take the 40 divide it by 10 so it is now in Bells thus 4 B and raise 10 to the power of the number Ie 10 4 = 10 x 10 x 10 x 10 or 10,000

15. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/14/21 Remember (or calculate) these 2^1 = 2 so log 2 (2)=1 2^2 = 4 so log 2 (4)=2 2^3 = 8 so log 2 (8)=3 2^4 = 16 so log 2 (16)=4 2^5 = 32 so log 2 (32)=5 2^6 = 64 so log 2 (64)=6 2^7 = 128 so log 2 (128)=7 10dB = 10:1 20dB = 100:1 30dB = 1000:1 40dB = 10,000:1 3dB = 2:1 6dB = 4:1 26dB = 400:1 NB Add dB, multiply the ratios

16. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/15/21 Example Tut Questions Q1: Given the ASCII code for the letter ‘F’ is 0x46 draw the binary pattern transmitted if the following data format is used –(a) One start bit, 8 data bits and one stop bit 8N1 –(b) One start bit, 8 data bits, even parity and one stop bit 8E1 –(c) One start bit, 7 data bits, odd parity and two stop bits 7O2 Ans1: [0100][0110] so b0, bit zero, the least significant bit is on right. Remember unfortunately data is transmitted bit zero first, usually drawn with bit zero on left if drawing square waves, also RS232 uses –12V for ‘1’, +12v for ‘0’ Note parity includes all data bits and the parity bit itself, so a data word of 0100 0110 would need a 1 added to give even parity, parity bits are added after bit 7 ( or bit 6)

17. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/16/21 Hex 0x46 is 0100 0110, we write binary bit zero on right Transmitted data XX__[0][1][1][0][0][0][1][0]XX +12 -12 0101 Start bit ‘0’ Stop bit of ‘1’

18. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/17/21 Now you can go and try Q1b and Q1c Be able to writing down the binary, calculating parity, adding stop and start bits and drawing the waveforms. Related Questions: Q2: Calculate how long in milliseconds it takes to send a 8N1 character at 1200 baud Q3: How long to send “HELLO_WORLD” at 9600 baud assuming 8E2 Q4: What is the overhead in sending a character in the format of 8N1? Q5, Book (ed 3) Q22, Q23, Pages 75 (see.pdf)

19. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/18/21 The formulae! Nyquist: When there is no noise… a perfect channel carrying ‘V’ levels Shannon: When we have noise… a signal to noise level of s/n

20. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/19/21 Tut questions (3 rd edition, p170-) Q2-3 Analogue TV channels are 6MHz wide, how many bits/sec can be sent if 4 level signals are used, ignoring noise Q2-4 A binary signal is sent over a 3kHz channel whose signal to noise ratio is 20dB, what is the maximum data rate possible Q6 If a modem uses 4 amplitude levels and 4 phase values how many different bits of information can be sent in a single data change. Q7 (a) If the signal to noise ratio in Q2-4 changes to 30dB what is the new maximum data rate? (b) for 36db?

21. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/20/21 Revision…I’ll repeat this Address the following areas in the recommended textbook general issues pp1-7 network hardware ring v buspp7-10 wide area networkspp11-16 network software - layerspp16-22 connection oriented / connectionlesspp22-27 services, protocols peers pp27-28 OSI reference model and layers pp28-34 TCP/IP pp35-39 Internet pp52-54 Standards who and why? pp67-72

22. 01/10/04 www.eej.ulster.ac.uk/~ian/modules/COM347J1/COM347J1_SUMS.ppt SUMS/21/21 Revision…I’ll repeat this Syn/asych transfer Physical layer - bandwidth limited pp86-87 baud v bits per secondpp88-89 Nyquist max data ratepp 89-90 Shannon’s max data ratepp 90 Media: (tape), UTP, Coaxial cable, FOC, Tx light, Light sources, Wireless, Radio,microwave,IR, pp 90-99 Modems baud v bps pp125-127 modulation methods pp127-130