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142 Fundamentals of Computers NPP

3.3 Octal Number System 3.3 Am°ŠQ>b Zå~a {gñQ>_
Octal number system uses eight distinct Am°ŠQ>b nÕ{V _| Hw$b AmR> {d{^ÝZ àH$ma Ho$ g§Ho$Vm|
symbols, 0, 1, 2, 3, 4, 5, 6, 7. The base of this H$m Cn`moJ hmoVm h¡Ÿ& `o AmŠQ>b A§H$ H$hbmVo h¢ Ÿ& `o h¢,
number system is 8. Any octal number can be 0, 1, 2, 3, 4, 5, 6, 7& Bgr{bE Am°ŠQ>b g§»`m nÕ{V
interpreted by multiplying the octal digit by H$m AmYma (~og) 8 h¡ Ÿ& {H$gr ^r Am°ŠQ>b g§§»`m Ho$ _mZ
its positional weight and adding all such H$mo g_PZo hoVw BgHo$ {d{^ÝZ A§H$m| H$mo AmR> H$s {d{^ÝZ
products. For example (431.62) can be KmVm| go JwUm H$aVo h¢ VWm Eogo àmá gmao JwUZ\$bm| H$mo
8
interpreted as: Omo‹S>Vo h¢ Ÿ& CXmhaU Ho$ {bE, (431.62) H$mo h_ Bg
Vah go g_P gH$Vo h¢… 8
2
4 × 8 + 3 × 8 + 1 × 8 + 6 × 8 + 2 × 8 -2
1
0
-1
while performing Conversion from octal O~ h_ Am°ŠQ>b g§»`m `o ~mBZar g§»`m àmá H$aZo
to Binary it is important to memorise 3-bit H$s H$mo{ee H$aVo h¢ VWm h_| àË`oH$ Am°ŠQ>b A§H$ Ho$ 3-
binary equivalent of each octal digit. You are {~Q> ~mBZar Vwë` H$s Amdí`H$Vm n‹S>Vr h¡ Ÿ& AV… Vm{cH$m
advised to memorise the following table 3.2:
3.2 H$mo AÀN>r Vah go `mX H$a boZm Mm{hE Ÿ&
Table 3.2
Octal digit 3 bit Binary Equivalent
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111
It is very important to learn the counting {H$gr ^r g§»`m nÕ{V _| JUZm H$m ~hþV _hËd h¡ Ÿ&
sequence in a number system. There is no 8 after
7 in octal number system. Because 8 is not a Am°ŠQ>b g§»`m nÕ{V _| eyÝ` go 7 VH$ {bIVo h¢Ÿ& BgHo$
symbol used by octal number system. Then what ~mX 8 Zht {bI gH$Vo Š`m|{H$ Bg Vah H$m H$moB© g§Ho$V
is the next number after 7? It is 10. How? Because
7 is the greatest number of single digit. The next Am°ŠQ>b _| Zht hmoVm Ÿ& AV… h_ 8 Ho$ ~OmE 0 {bIVo
digit will be the smallest digit, that is '0' h¢ Am¡a EH$ hm{gb boVo h¢ Ÿ& AV… AJbr g§»`m 10 hmoJrŸ&
generating a carry to the left. After 10 the next
number is 11, then 12 and so on. BgHo$ ~mX 11, 12, Am{X Ÿ&
What is the next number after 17 ? It is 20 àíZ CR>Vm h¡ {H$ Am°ŠQ>b _| 17 Ho$ ~mX Š`m ?
because the next digit after 7 is '0' and add BgH$m CÎma h¡, 20 Š`m|{H$ 7 Ho$ ~mX eyÝ` {bIZm hmoJm
carry to '1'. Thus first few numbers of octal
number system can be written as: Am¡a EH$ hm{gb H$m boZm hmoJm Ÿ& Bgr Vah go Am°ŠQ>b
g§»`m nÕ{V Ho$ àW_ Hw$N> Zå~a ZrMo Xem©E JE h¢…