Number system | Grade 10 | ICT Tamil Presentation By Raza Malhardeen

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Grade 10 | Chapter No. 03 | Lesson Title : Number system
Tamil Medium

ghlcs;slf;fk;
• 3.1 vz; Kiwikfs; (Number system)
• 3.2 vz; Kiwikfs;
• 3.3 ,Uk> vz;k> gjpd;k> gjpdWkvz; Kiwfs;
– gjpd;k vz; Kiwik(Decimal number system)
– ,Uk vz; Kiwik(Binary number system)
– vz; Kiwik(Octal number System)
– gjpdWk vz; Kiwik(Hexadecimal number system)

• 3.4vz; KiwikfSf;fpilapyhdgupkhw;wk;
– gjpd;kvz;fis,Ukvz;fshfkhw;Wjy;(10-2)
– gjpd;kvz;fisvz;k vz;fshfkhw;Wjy;(10-8)
– gjpd;kvz;fisgjpdWkvz;fshfkhw;Wjy;(10-16)
• 3.5vz; KiwikfSf;fpilahdkhw;wPL
– ,Ukvz;fisgjpd;k vz;zhfkhw;Wjy;
– ,Ukvz;fisvz;k vz;fshfkhw;Wjy;
– ,Ukvz;fisgjpdWkvz;fshfkhw;Wjy;
• 3.6vz;k vz;fisgjpd;k>,Ukvz;fshf khw;Wjy;
– vz;k vz;fisgjpd;kvz;fshfkhw;Wjy
– vz;k vz;fis,Ukvz;fshfkhw;Wjy;
• 3.7gjpdWkvz;fisgjpd;k>,Ukvz;fshfkhw;Wjy;
– gjpdWkvz;fisgjpd;kvz;fshfkhw;Wjy;
– gjpdWkvz;fis,Ukvz;zhf khw;Wjy;

• 3.8 juTNjf;ffq;fis(data Storage) mstPLfSf;Fg;gad;gLj;jy;
• 3.9 fzpdpapy; gad;gLj;jg;gLk;FwpaPl;LKiwfs;
– m];fp ASCII FwpaPl;L Kiw
– BCD (Binary coded decimal)FwpaP l; L Kiw
– EBCDIC (Extended Binary coded decimal
interchange code)
– AdpNfhl; (Unicode) Kiw

,e;j mj;jpahaj;ijf;fw;gjd;%yk; ePq;fs;
• vz; Kiwikfspd; gpd;dzpAk;> tuyhWk;
• gy;NtW vz; Kiwikfs; (Bin., Oct., Des., Hex des)
• ,Uk> vz;k> gjpd;k> gjpdWk vz; Kiwikfs;
• vz; Kiwik tiffSf; fpilapyhd khw;wk;
• juTfis Njf;Ftjw;Fg; (Store) gad;gLj;Jk;myFfs;
• fzpdpfspy; gad;gLj;jg;gLk;FwpKiwg; gLj;jy;(coding system) Kiwfs;
Mfpad gw;wpatpsf;fj;ijg;ngw;Wf; nfhs;s KbAk;.

• ve;jnthU ngWkhdj;ijAk; Fwpg;gplj;jf;f jdpj;Jtkhd FwpaPLfs; my;yJ vz;
njhilNa vz; Kiwik vdg;gLk;. cjhuzkhf gjpd;k vz; Kiwik 0 njhlf;fk; 9 tiuahd
vz; njhilahy; Mf;fg;gl;ljhFk;.
• fPNo> vz; Kiwikfs; gad;gLj;jg;gLk;re;ju;g;gq;fs; rpy jug;gl;Ls;sd.
– —ngWkhdq; fis tifFwpj; Jf; fhl; ly;
– —vz;Zjy;
– —fzpj;jy;fis Nkw;nfhs;sy;
– —ngWkhdq;fis xg;gply;
– —ngWkhdq;fis xOq;FKiwapy; tupirg;gLj;jy;
3.1 vz; Kiwikfs; (Number system)

3.2 vz;Kiwikfs;
• ve;jnthU ngWkhdj;ijAk; Fwpg;gplj;jf;fjdpj;JtkhdFwpaPLfs; my;yJ vz;njhilNa vz;
Kiwikvdg;gLk; .
• cjhuzkhf
• gjpd;k vz;Kiwik0 njhlf;fk; 9 tiuahd vz;njhilahy; Mf;fg;gl;ljhFk;.
• fPNo> vz;Kiwikfs;gad;gLj;jg;gLk; re;ju;g;gq;fs; rpyjug;gl;Ls;sd.
– —ngWkhdq;fis tifFwpj;Jf; fhl;ly;.
– —vz;Zjy;.
– —fzpj;jy;fis Nkw;nfhs;sy;.
– —ngWkhdq;fis xg;gply;.
– —ngWkhdq;fis xOq;FKiwapy; tupirg;gLj;jy;.

3.3 ,Uk>vz;k> gjpd;k>gjpdWkvz; Kiwfs;
vz; Kiwik mb Numbers & Alphabet Used
1 ,Uk(Jtpj) Binary 2 0 1
2 vz;k Octal 8 0 1 2 3 4 5 6 7
3 gjpd;k (jrk) Decimal 10 0 1 2 3 4 5 6 7 8 9
4 gjpdWk Hexa-
decimal
16
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 1 2 3 4 5 6 7 8 9 A B C D E F
Only Number system using by Human is Decimal (10) Number System
Only Number system using by Computer is Binary (2) Number System

gjpd;k(jrk) vz; Kiwik
• Decimal number system

104 103 102 101 100 10-1 10-2 10-3
10000 1000 100 10 1 .1 .01 .001

• md;whleltbf;iffspy; gjpd;kvz; KiwikiaNaehk;gad;gLj;Jtjdhy;
gjpd;k vz; Kiwikapy; vz;Zf;F fPNombg;ngWkhdk;vOjg;glj;
Njitapy;iy. vdpDk; > Vida vz; Kiwikfspy; Fwpg; gpl;l vz;fSf;Ff;
fPo; mtw;wpw;Fupambg; ngWkhdq;fs; fl;lhakhfvOjg;gl
Ntz;Lk;.
Ex
2010 1012 AF16No Need to
write If 10 base

• 25 vDk; vz; vt;thWcUthfpaJ
25 = 20 + 5
= (2 x 101) + (5 x 100)
= (2 x 10) + (5 x 1)
102103104105 100101

,q;F 100> 101>102 vDk;vz;fs;gjpd;kvz; (Decimal Numbers) Kiwikapd;kjpg;Ngw;Wq;fhuzpfs;
(Weighting factors) vd miof;fg;gLk;.
125vd;w vz;iz gpd;tUkhWfhl;lyhk;:
1 2 5
kjpg;Ngw;Wq;fhuzpfs; 102 101 100
5 x 100
2 x 101
1 x 102
= 5 x 1
= 2 x 10
= 1 x 100
= 5
= 20
= 100
125
gjpd;k vz;;

1 2 5 . 4 5
kjpg;Ngw;Wq;fhuzpfs;
102 101 100 10-1 10-2
2 x 10-2
1 x 10-1
5 x 100
2 x 101
1 x 102
= 5 x 1/100
= 4 x 1/10
= 5 x 1
= 2 x 10
= 1 x 100
= 0.05
= 0.4
= 5
= 20
= 100
125.45
gjpd;k vz;;

,Uk vz; Kiwik
• Binary number system

• kpd;dpay; cgfuzkhdfzpdpf;Fkpd;tYtoq;fg;gl;lhy; kl;LNknjhopw;gLk;.mjhtJ>
,q;Fkpd;Ndhl;lk; cz;L>,y;iy vDk;,uz;Lre;ju;g;gq;fs;fUj;jpw;nfhs;sg;glj;jf;fdthf
cs;sd. ,t;thNw
• kpd;Fkpnohd;iwf;fUj;jpw;nfhs;Nthkhapd;kpd;Fkpo;vupjy;>mizjy;vDk;
,uz;Lre;ju;g;gq;fs;cs;sd.mjhtJ'cz;L">',y;iy" vDk; ,uz;LepiyfSNkmitahFk;.
• ,e;j,uz;LepiyfSf;F1>0Mfpa,uz;LngWkhdq;fisAk; gpujpaPLnra;Nthnkdpd;
,uz;L,yf;fq;fs; nfhz;lvz;Kiwikiag; ngw;Wf;nfhs;syhk;.

• ,t;thwhdvz; njhFjp ,Ukvz; Kiwikvdg;gLk;.
• ,uz;ilmbahff;nfhz;lvz;njhFjpapy;0>1Mfpa,yf;fq;fs;kl;LNkgad;gLj;jg;gLk;.
• 20>21>22>23…Mfpa vz;fs; ,uz;il mbahff; nfhz;l vz;Kiwikapd;kjpg;Ngw;Wq;
fhuzpvdg;gLk;.

1012 vDk; vz;izf; fUJf.
1 0 1
,Ukvz;;

vz;k vz; Kiwik
• Octal number system

• ,e;j vz;njhFjpapy; 0 - 7 tiuahdvl;L ,yf;fq;fs; gad;gLj;jg;gLk;.
• ,jd; mbg; ngWkhdk;(base Value) 8 MFk;.
• ,q;F 80>81>82>83… Mfpa vz;fs; vz;k vz; Kiwikapd;
kjpg;Ngw;Wq;fhuzpfs;(weighting factors) vdg;gLk; .

1268 vDk; vz;izf; fUJf.
1 2 6
vz;k vz;;

gjpdWk vz; Kiwik
• Hexa-Decimal number system

• ,t;ntz; Kiwikapy; 0 - 9 tiuahdgj;J,yf;fq;fSk; A-F tiuahdMW
FwpaPLfSk; gad;gLj;jg;gLk;.
• ,jd; mb 16 MFk;.
• ,q;F 160>161>162… Mfpa vz;fs; gjpdWk vz; Kiwikapd;
kjpg;Ngw;Wq; fhuzpfs;vdg;gLk;

1316vDk; vz;izf; fUJf.
1 3
kjpg;Ngw;Wq;fhuzpfs; 161 160
gjpdUk vz;;
3EF16vDk; vz;izf; fUJf.
3 E F
gjpdUk vz;;

gjpd;kvz;fis ,Ukvz;fshf khw;Wjy;
• ,t; vz;iz G+r;rpak; (0) kPjpahftUk; tiu,uz;bdhy; (2) njhlu;e;J
tFf;fTk;.fpilf;fg;ngw;wkPjpfisfPopUe;J NkyhfxOq;F Kiwapy;
vOJf.

Example 1
• 810 ,Uk vz;fshf khw;Wjy;
8
4
2
1
0
-
-
-
-
0
0
0
1
2
2
2
2
810 = 10002

Example 2
• 23 ,id ,Uk vz;zhfkhw;wpmjd; kpf mjpfkjpg;GW ,yf;fj;ijAk;
kpff;Fiwe;jkjpg;GW ,yf;fj;ijAk; fzpf;f.
23
11
5
2
1
-
-
-
-
1
1
1
0
2
2
2
2
0
-
- 1
2
2310 = 101112
LSD
MSDLSDMSD

,jd; NghJ tUk; tpilapd;
• ,lJ me;jj;jpy; cs;s G+r;rpaky;yhj ngWkhdk;kpf mjpf kjpgG;W
,yff;k; (MSD - Most significant digit) vdTk;
• tyJ gf;fj;jpYs;s ngWkhdk;(tyJ gff;jj;py;jrkg; Gs;spfF; kpf
mz;ikapYs;s ngWkhdk;) kpff;Fiwej; kjpgG;W ,yf;fk; (LSD -
Least significant digit) vdTk; miof;fg;gLk;.

10011011 111011000 10100011

&

gjpd;kvz;fis vz;k vz;fshf khw;Wjy;
• kPjp G+r;rpakhFk; tiu ,t; vz;iz vl;L(8) ,dhy;
njhlu;e;J tFf;fTk; fpilf;Fk; kPjpfis fPopUe;J
Nkyhf tupirapy; vOJf.
8
1
0
-
-
0
1
8
8
810 = 108
Eg1: 810 = ?

19
2
0
-
-
3
2
8
8
1910 = 238
Eg2: 1910 = ? Change 10 to base 8
103
12
1
-
-
7
4
8
8
10310 = 1478
Eg3: 10310 = ?
0 - 1
8
kPjp
kPjp

gjpd;kvz;fis gjpdWkvz;fshf khw;Wjy
• ,q;F kPjpG+r;rpakhFk; tiu 16 ,dhy; tFj;J tUk; kPjpfis fPopUe;J
Nkyhf tupirapy; vOJf.
16
1
0
-
-
0
1
16
16
1610 = 1016
Eg1: 1610 = ?
kPjp

33
2
0
-
-
1
2
16
16
1910 = 2116
Eg2: 3310 = ? Change 10 to base 16
kPjp
60
3
0
-
-
12
3
16
16
6010 = 3C16
Eg3: 6010 = ?
kPjp
C
,q;F 60 I 16 ,dhy; tFf;Fk;NghJ tUk; kPjp 12 MFk;. Mdhy; > ,q;F 9 I tplf; $ba vz;fis
vOjKbahJ. MfNt> 12 ,w;F gjpyhf C vDk; FwpaPL gad;gLj;jg;gLk;.

239
14
0
-
-
15
14
16
16
23910 = 151416 = EF16
Eg4: 23910 = ?
Change 10 to base 16
257
16
1
-
-
1
0
16
16
25710 = 10116
Eg5: 25710 = ?
0 - 1
16
kPjp
kPjp
F
E

• NkNy ehk;gjpd;k vz;fis
– ,Uk vz;zhf
– vz;k vz;zhf
– gjpdWk vz;zhf
khw;WtJ gw;wpf; fw;Nwhk;.
 ,dp ehk;
,Uk>
vz;k>
gjpdWk vz;fis
gjpd;k vz;zhf khw;Wk; Kiwia mwpe;J nfhs;Nthk;.

,Ukvz;fis gjpd;kvz;zhf khw;Wjy;
,q;F 20> 21> 22 vDk;vz;fs; gjpd;k vz; (Binary Numbers) Kiwikapd;
kjpg;Ngw;Wq;fhuzpfs;(Weighting factors) vdmiof;fg;gLk;.
,jidg; gpd;tUkhWfhl;lyhk;:
1 1
kjpg;Ngw;Wq;fhuzpfs; 21 20
1 x 20 = 1 x 1 = 1
gjpd;k vz;;
= 3
Ex1: 112=
112= 310
1 x 21 = 1 x 2 = 2
Change 2 to base 10

112 = (1 X 21) + (1 X 20)
= (1 X 2 ) + (1 X 1)
= 2 + 1
= 3
So, 112 = 310
1 1
kjpg;Ngw;Wq;fhuzpfs;21 20
gjpd;kvz;;
Change 2 to base 10

Ex2: 10112
1 0 1 1
23 22 21 20
10112 = (1x 23) + (0x22) + (1x 21) + (1x20)
= (1x8) + (0x4) + (1x2) + (1x1)
= 8 + 0 + 2+ 1
= 11
So, 10112 = 1110
Change 2 to base 10

vz;Kiwikml;ltiz
16 10000 20 10
17 10001 21 11
18 10010 22 12
19 10011 23 13
20 10100 24 14
21 10101 25 15
22 10110 26 16
23 10111 27 17
Number system Table
Decimal
(10)
Binary
(2)
Octal
(8)
Hexa-
decimal
(16)
0 0000 0 0
1 0001 1 1
2 0010 2 2
3 0011 3 3
4 0100 4 4
5 0101 5 5
6 0110 6 6
7 0111 7 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
EXTRA

0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1

,Ukvz;fis vz;k vz;fshf khw;Wjy;.
• Kjypy; tyJ gf;f me;jj;jpypUe;J ,lJ gf;f me;jk;tiu %d;Wvz;fs; nfhz;ljhfg; gpupj;J vOjpf;
nfhs;Sq;fs;.
• xt;nthU njhFjpf;Fupa vz;kvz;izKiwNa vOJq;fs;.
• gpd;du;>mt;ntz;fis ,lkpUe;J tykhf Nru;j;J tupirapy; vOjpf; nfhs;Sq;fs;.
Change 2 to base 8
EX1: 1011002
101100
101 100
5 4 = 548

EX2: 110011012
11001101
11 001 101
3 1 5 = 3158
So, 110011012 = 3158

,Ukvz;fis gjpdWkvz;fshf khw;Wjy;.
• ,q;FKd;diug;Nghd;W…
• tyJ gf;fj;jpypUe;J ,lJ gf;fk; tiu ehd;F ,yf;fq;fs; nfhz;l njhFjpfshfg; gpupj;J vOjpf;nfhz;l
gpd;du;
• mt; vz;njhFjpfSf;fhd gjpdWk vz;fis vOJf.
• gpd;du; mt; vz;fistyJ gf;fj;j;pypUe;J ,lJ gf;fk; tiu tupirapy; vOjpf;nfhs;f.
Change 2 to base 16
EX1: 101012 10101
1 0101
1 5 = 1516

EX2: 11101010112
1110101011
11 1010 1011
3 12 13
= 3AB16A B3
So, 11101010112 = 3AB16
Change 2 to base 16

• 3.6.1vz;kvz;fisgjpd;kvz;fshfkhw;Wjy;
• 3.6.1 vz;kvz;fis,Uk
• vz;fshfkhw;Wjy;
3.6 vz;kvz;fis gjpd;k> ,Ukvz;fshf khw;Wjy;

Change 8 to base 10
108 = (1 X 81) + (0 X 80)
= (1 X 8 ) + (0 X 1)
= 8 + 0
= 8
So, 108 = 810
1 0
gjpd;kvz;;
EX1: 108
3.6.1 vz;k vz;fis gjpd;kvz;fshf khw;Wjy;

Change 8 to base 10
EX2: 1478
108 = (1 X 82) +(4 X 81) + (7 X 80)
= (4 X 16 ) + (4 X 8) + (7 X 1)
= 64 + 32 + 7
= 103
So, 1478 = 10310
1 4 7
kjpg;Ngw;Wq;fhuzpfs;82 81 80
gjpd;kvz;;

vz;k vz;fis ,Ukvz;fshf khw;Wjy;
• Kjypy; vz;kvz;fSf;Fk;,Uk vz;fSf;Fk;
,ilapyhd njhlu;ig
mwpe;Jnfhs;Nthk;. (ml;ltiz)
• vz;kvz;fis,Uk vz;fshf Fwpg;gpLk;NghJ
mg;ngWkhdq;fs;
%d;W,yf;fq;fisf; nfhz;ljhf ,Uf;Fk;. (8=
23 Mifahy;)
•
Binary
(2)
Octal
(8)
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7
Change 8 to base 2
Decimal
(10)
Binary
(2)
Octal
(8)
Hexa-
decimal
(16)
0 0000 0 0
1 0001 1 1
2 0010 2 2
3 0011 3 3
4 0100 4 4
5 0101 5 5
6 0110 6 6
7 0111 7 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F

Change 8 to base 2
EX1: 238
238 = (010 011)2
= 0100112
So, 238 = 0100112
2 3
Binary
(2)
Octal
(8)
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7
010 011
EX1: 3458
3458 = (011 100 101)2
= 0111001012
So, 3458 = 0111001012
3 4 5
011 100 101
,q;F jug;gl;l vz;zpYs;s xt;nthU ngWkhdj;Jf;Fnkd ,Uk vz; ngWkhdq;fis %d;W gpl;fspy;
vOJf

• 3.7.1gjpdWkvz;fisgjpd;kvz;fshf khw;Wjy;.
• 3.7.2gjpdWkvz;fis,Ukvz;zhf khw;Wjy;.
3.7 gjpdWkvz;fis gjpd;k>,Uk vz;fshf
khw;Wjy;

.
3.7.1 gjpdWkvz;fis gjpd;kvz;fshf khw;Wjy;.
2016 = (2 X 161) + (0 X 160)
= (2 X 16 ) + (0 X 1)
= 32 + 0
= 32
So, 2016 = 3210
2 0
gjpd;kvz;;
EX1: 2016
3D16 = (3 X 161) + (D X 160)
= (3 X 16 ) + (13 X 1)
= 48 + 13
= 61
So, 2016 = 6110
3 D
gjpd;kvz;;
EX2: 3D16

.
FF16 = (F X 161) + (F X 160)
= (15 X 16 ) + (15 X 1)
= 240 + 15
= 255
So, FF16 = 25510
F F
gjpd;kvz;;
EX3: FF16

3.7.2 gjpdWkvz;fis ,Ukvz;zhf khw;Wjy;.
• gjpdWk vz;zhfkhw;Wk; NghJ
mt;ntz;zpYs;s xt;nthU vz;izAk; my;yJ
FwpaPl;ilAk;ehd;F ,yf;fq;fspy; fhl;l
Ntz;Lk;.(24=16 Mifahy;)
• ,g;NghJ gjpd;k vz;fs;> gjpdWk vz;fs; ,Uk
vz;fs; Mfpatw;Wf;F,ilapyhd njhlu;ig
mwpe;J nfhs;Nthk;.
Decimal
(10)
HexaDeci
mal (16)
Binary
(2)
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
Change 16 to base 2

Decimal
(10)
Hexadec
imal (16)
Binary
(2)
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
Change 16 to base 2
EX1: 8716
8716 = (1000 0111)2
= 100001112
So, 8716 = 100001112
8 7
1000 0111
EX2: 3C16
3C16 = (0011 1100)2
= 001111002
So, 3C16 = 00111100 2
3 C
0011 1100

Decimal
(10)
Hexadec
imal (16)
Binary
(2)
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
Change 16 to base 2
EX3: 8EC16
8EC16 = (1000 1110 1100)2
= 100011101100 2
So, 8EC16 = 100011101100 2
8 E C
1000 1110 1100
,q;F>E apd; ngWkhdk; 14 MFk;.mq;F,Uk vz;ngWkhdk;1110 MFk;.
Capd; ngWkhdk; 12 MFk;.mq;F ,Uvz;ngWkhdk; 1100 MFk;.

Accepting your valuable comments, suggestions and let
me know if any correction to be done …
உங்கள் கருத்துகளையும் ஆல ோசளைகளையும் எதிர்போர்கி்றலன்ற,
திருத்தங்கள் இருந்தோலும் அனியத் தர ோம்
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Or Email: mraza.edu@gmail.com
Thank for All

Special Thanks
NIE – National institute of Education, Sri Lanka
Edited By
Raza Malhardeen (mraza.edu@gmail.com)
Comments & ContactTHE END
Thank You

Number system | Grade 10 | ICT Tamil Presentation By Raza Malhardeen

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