Page 140 - FUNDAMENTALS OF COMPUTER

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140 Fundamentals of Computers NPP

Number System g§»`m nÕ{V
"A number system uses r distinct symbols “EH$ g§»`m nÕ{V _| r {d{dY g§Ho$Vm| H$m Cn`moJ
to represent r digits".
{H$`m OmVm h¡, {OÝh| r A§H$ H$hVo h¢ Ÿ&''
3.1 Base (Radix) 3.1 AmYma
The total number of distinct symbols used {H$gr g§»`m nÕ{V _| Hw$b A§H$m| H$s g§»`m H$mo
by a number system is called its Base or Radix. CgH$m AmYma H$hVo h¢ Ÿ& CXmhaUV… Xe_bd g§»`m
For example our decimal number system uses nÕ{V _| ZrMo Xem©`o g§Ho$V (A§H$) Cn`moJ _| bmE OmVo h¢…
following distinct symbols :
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Therefore decimal number system is a Base Bg{bE Xe_bd g§»`m nÕ{V H$m AmYma 10 h¡ Ÿ&
10 number system. In every number system, àË`oH$ g§»`m nÕ{V _| A§H$m| H$s H${‹S>`m| go hr g§»`mE±
the numbers are formed by string of digits. To ~ZVr h¢& {H$gr g§»`m H$m _mZ g_PZo Ho$ {bE CgHo$
inteprete any number we must multiply each
digit by some positive or negative integer àË`oH$ A§H$ H$mo AmYma r H$s Hw$N> YZmË_H$ `m F$UmË_H$
power of r and add, for example 213.547 can be KmV go JwUm H$aHo$ g^r H$mo Omo‹S>Zm hmoVm h¡ Ÿ& O¡go 213.547
interpreted as : H$mo Bg Vah go {bI gH$Vo h¢ Ÿ:
1
2
-2
-1
0
2 × 10 + 1 × 10 + 3 × 10 + 5 × 10 + 4 × 10 + 7 × 10 -3
It means 2 hundreds, plus 1 tens, plus 3 Bggo VmËn`© h¡, 3 BH$mB© , 1 XhmB© Am¡a 2 g¡H$‹S>m
units plus 5 tenths, plus 4 hundredth plus 7 VWm 5 Xjm§e, 4 gm¢ do ^mJ VWm 7 hOmad| ^mJ Ÿ& g§{já
thousandth. The shortcut here is move away _| BgH$mo Bg Vah go `mX aI gH$Vo h¢ : h_oem Xe_bd
from the decimal point. In integer part start
from a zero power and increment by one as q~Xw go Xya OmAm| Ÿ& nyUmªH$ _| KmV eyÝ` go ewê$ H$aHo$
you move from one digit to another. In fractional EH$-EH$ ~‹T>mVo OmAmo Ÿ& AnyUmªH$ _| KmV -1 go ewê$ H$a
part start from –1 and increment by one as you EH$-EH$ go ~‹T>mVo OmAmo Ÿ& O¡go -1, -2, -3, Am{X Ÿ&
move from one digit to another. The following ZrMo ~ZmE {MÌ H$mo `mX aImo:
diagram will help you remember the trick :

2 1 3 . 5 4 7
10 2 10 1 10 0 10 –1 10 –2 10 –3
3.2 Binary Number System 3.2 ~mBZar Zå~a {gñQ>_

This number system uses only two distinct Bg g§»`m nÕ{V _| {g\©$ Xmo g§Ho$Vm| 0 Ed§ 1 H$m
symbols '0' and '1'. Therefore base (Radix) of Cn`moJ {H$`m OmVm h¡ Ÿ& Bgr{bE Bg nÕ{V H$m AmYma 2
this number system is 2. The internal Circuit h¡ Ÿ& H$åß`yQ>a Ho$ n[anW _| ~mBZar nÕ{V H$m Cn`moJ hmoVm
of the computer normally uses binary number
system. The symbols '0' and '1' are called h¡Ÿ& 0 Am¡a 1 H$mo ~mBZar {S>{OQ> ({~Q>) H$hVo h¢ Ÿ& O¡go,
Binary Digits (Bits). Thus, 1001 is a 4-bit 1001 EH$ 4-{~Q> ~mBZar g§»`m h¡ Ÿ& BgH$m ^ma Bg Vah
binary number. The interpretation of this go {ZH$mbm Om gH$Vm h¡ :
number is as:
1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 = 9
0
2
3
1