Page 156 - FUNDAMENTALS OF COMPUTER

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156 Fundamentals of Computers NPP

(b) The given Hexadecimal Number (3F2) 16 (b) (3F2) H$mo hoŠgmS>o{g_b go Xe_bd _| Bg
16
can be converted into decimal with the help of Vah go àmá {H$`m Om gH$Vm h¡…
following procedure:
3 F 2
16 2 16 1 16 0
768 + 240 + 2 = 1010
Note : F = 15 is taken for the multiplication ZmoQ>: F = 15 boH$a 16 go JwUm {H$`m J`m Ÿ&
with 16. '
Thus, (3F 2) = (1010) 10
16
(c) The given Hexadecimal number 10. A3 (c) {X`m J`m 10.A3 hoŠgmS>o{g_b Z§~a {_{lV
is a mixed number. Its decimal equivalent can g§»`m h¡Ÿ& BgHo$ S>o{g_b BpŠddob|Q> H$s JUZm {ZåZ
be calculated as below :
àH$ma go H$s Om gH$Vr h¡:
1 0 . A 3
16 1 16 0 16 -1 16 -2
10 3 163
16 + 0 + + = 16 +
16 256 256
Or, 16 . 63
Thus, (10.A3) = (16.63) 10
16
(d) The Decimal value of (.41) is as (d) (.41) H$m Xe_bd _mZ Bg àH$ma h¡ …
16
16
follows :
. 4 1
16 -1 16 -2
4 1
16 + 256 = .25
Thus, (.41) = (.25) 10
16
Some More Conversions Hw$N> Am¡a H$ÝdO©Z
If a number is given whose base is r, it can `{X H$moB© ^r g§»`m Xr JB© hmo {OgH$m AmYma r h¡ Vmo
be converted to decimal using the formula Bgo {ZåZ{b{IV gyÌ H$s ghm`Vm go Xe_bd _| ~XbVo h¢…
shown below:

0
-3
-2
-1
1
2
(xyz. pqr) = (x × r + y × r + z × r + p × r + q × r + r × r ) 10
r
Consider the following problems : A~ {ZåZ{b{IV g_ñ`mAm| H$mo g_Pmo …
Problem 3.15 àíZ 3.15
Convert the following numbers with Xem©E JB© AmYma dmbr g_ñ`mAm| H$mo Xe_bd _|
indicated base to decimal :
~Xbmo…
(a) (230) 5 (b) (14.22) 6 (c) (0.121) 3 (d) (46.78) 9