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NPP Number System, Boolean Algebra and Logic Circuits 145

Use of Hexadecimal number hoŠgmS>o{g_b g§»`mAm| Ho$ Cn`moJ
Hexadecimal number system is used in hoŠgmS>o{g_b Agoå~br ^mfm _| àmoJ«mq_J H$aVo g_`
assembly language programming. The H$m_ _| AmVo h¢ Ÿ& Bg ^mfm _| h_ {ZX}em| d S>mQ>m H$mo
instructions and data are entered as Hexadecimal
numbers because instruction code and data are hoŠgmS>o{g_b _| {bIH$a àXmZ H$aVo h¢ Š`m|{H$ ~mBZar _|
very lengthy in binary form. Each Hexadecimal {bIZo na b§~mB© ~hþV Á`mXm hmo OmVr h¡& àË`oH$
digit is converted into 4-bit numbers. hoŠgmS>o{g_c A§H$ 4 {~Q> _| ~Xc OmVm h¡Ÿ&
3.5 Conversion from Decimal to any Base 3.5 Xe_bd go {H$gr ^r AmYma _| ~XbZm
Suppose a decimal number is given and AJa AmnH$mo H$moB© Xe_bd g§»`m Xr JB© hmo Am¡a
you are asked to find its equivalent in a number {H$gr Xygao AmYma r dmbr g§»`m nÕ{V _| ~XbZo H$mo
system whose base is r. (r = 2 for Binary, r
= 8 for octal, r = 16 for Hexadecimal). The H$hm J`m hmo (r = 2 (~mBZar) , r = 8 (Am°ŠQ>b), r = 16
process of conversion is different for integer (hoŠgmS>o{g_b) ) V~ nyUmªH$ d AnyUmªH$ XmoZm| {hñgm| Ho$
part and fractional part. The table shown below {bE AbJ-AbJ {d{Y`m| H$m Cn`moJ hmoVm h¡ Ÿ& BZ {d{Y`m|
gives details of the procedure: H$mo AmJo Xem©B Vm{cH$m 3.4 _| {X`m J`m h¡ Ÿ&
Table 3.4 Vm{cH$m 3.4

Decimal to Any Base (r) Conversion Xe_cd AmYma r _| ~XcZm
Integer part nyUmªH$
* Divide by the Base r. * r go ^mJ Xmo
* Write the quotient below and remainder * ^mJ\$b H$mo ZrMo {bImo d eof\$b H$mo grYo hmW
at the right hand side.
H$s Va\$ {bIm| Ÿ&
* Repeat the same procedure until the * Bgr {H«$`m H$mo XmohamAmo O~ VH$ {H$ ^mJ\$b
quotient becomes zero. eyÝ` Z Am OmE Ÿ&

* Read the remainders from bottom to top. * eof\$bm| H$mo ZrMo go D$na n‹T>mo Ÿ&
* This is the result.
* `ht n[aUm_r g§»`m h¡ Ÿ&

Fractional Part AnyUmªH$
* Multiply by r. * r go JwUm H$amo Ÿ&
* Write the fractional part of the product * JwUZ\$b Ho$ Am§{eH$ {hñgo H$mo ZrMo VWm nyUmªH$
below and the integer at right hand side.
dmbo {hñgo H$mo grYo hmW H$s Va\$ {bImoŸ&
* Repeat the same procedure until the * Bgr {H«$`m H$mo XmohamAmo O~ VH$ {H$ Am§{eH$ {hñgm
product becomes zero. (or stop after few
places of point). eyÝ` Z hmo Ÿ& (`m Hw$N> A§H$m| Ho$ ~mX éH$ OmAmo)&
* Read the integer parts from top to * nyUmªH$ dmbo {hñgo H$mo D$na go ZrMo n‹T>moŸ&
bottom and place a leading point.
* This is the result. * `hr n[aUm_r g§»`m h¡ Ÿ&