Page 155 - FUNDAMENTALS OF COMPUTER

NPP Number System, Boolean Algebra and Logic Circuits 155

(b) The given octal number is a purely (b) 0.31 EH$ nyU©V… Am§{eH$ am{e h¡ Ÿ& BgH$m
fractional number. Its decimal equivalent can Xe_bd Vwë` Bg àH$ma go {ZH$mbm Om gH$Vm h¡ Ÿ&
be calculated as below :
0. 3 1
8 -1 8 -2
3 1 25 = .39
8 + 64 = 64
Thus (0.31) = (0.39) 10
8
(c) The given octal number 62.101 is a (c) 62.101 EH$ {_{lV Am°ŠQ>b g§»`m h¡ {OgH$m
mixed number. The decimal equivalent can be Xe_bd Vwë` Bg àH$ma go àmá {H$`m Om gH$Vm h¡ …
calculated as below :
6 2 .1 0 1
8 1 8 0 8 -1 8 -2 8 -3
1 1
48 + 2 + + 0 + = 50.126
8 512
Thus, NPP (62.101) = (50.126) 10
8
Hexadecimal to Decimal Conversion hoŠgmS>o{g_b go S>o{g_b _| H$ÝdO©Z
The base of Hexadecimal number system hoŠgmS>o{g_b g§»`m nÕ{V H$m AmYma 16 h¡,
is 16. Therefore to convert a given Hexadecimal Bgr{bE gmar g§»`m H$ÝdO©Z _| 16 H$m Cn`moJ H$a|Jo Ÿ&
number into decimal we use 16 for all the
calculations. But it is very important to bo{H$Z `hm± EH$ ~mV `mX aIZm Amdí`H$ h¡ {H$ O~ ^r
remember that whenever, digit "A" comes in hoŠgmS>o{g_b g§»`m _| A AmE BgH$m _mZ 10 aI|, B
hexadecimal number put its decimal equivalent AmE Vmo 11 aI|, Bgr Vah F AmE Vmo 15 aI|Ÿ& ZrMo
10 for the calculation, whenever "B" comes put Xem©B© JB© g_ñ`mAm| go `h EH$X_ ñnîQ> hmo OmEJm…
11 and so on. The following examples will
illustrate the proce-dure:
Problem 3.14 àíZ 3.14
Convert following Hexadecimal number {ZåZm§{H$V hoŠgmS>o{g_b g§»`mAm| H$mo Xe_bd _|
into decimal :
~Xbmo…
(a) (98) 16 (b) (3F2) 16 (c) (10.A3) 16 (d) (0.41) 16
Solution : hc :

(a) The given Hexadecimal number (98) 16 (a) hoŠgmS>o{g_b g§»`m (98) H$mo ZrMo Xem©B© {d{Y
16
can be converted into decimal with the help of Ho$ AZwgma Xe_bd _| ~Xbm Om gH$Vm h¡:
the following procedure:
9 8
16 1 16 0
144 + 8 = 152
Thus, (98) = (152) 10
16