Page 157 - FUNDAMENTALS OF COMPUTER

NPP Number System, Boolean Algebra and Logic Circuits 157

Solution : hc :
(a) The given number 230 has a base equal (a) Xr JB© g§»`m 230 H$m AmYma 5 h¡ Ÿ& AV…
to 5. Therefore the decimal equivalent can be BgH$m Xe_bd _mZ Bg àH$ma h¡ …
calculated as follows :
⇒ 2 × 5 + 3 × 5 + 0 × 5 0
1
2
⇒ 50 + 15 + 0
⇒ 65
Thus, (230) = (65) 10
5
(b) The decimal equivalent of the mixed (b) {_{lV g§»`m (14.22) H$m Xe_bd _mZ Bg
6
number (14.22) can be calculated as below: àH$ma h¡…
6
1 4 . 2 2
6 1 6 0 6 -1 6 -2

2 2
6 + 4 + + + = 10.38
6 36
Thus, NPP (14.22) = (10.38) 10
6
(c) The given number (0.121) is a purely (c) (0.121) EH$ nyU©V… Am§{eH$ g§»`m h¡ {OgH$m
3
3
fractional number with base 3. The Decimal AmYma 3 h¡& AV… BgH$m Xe_bd Vwë` Bg àH$ma go àmá
equivalent can be calculated as below :
{H$`m Om gH$Vm h¡ …
0 . 1 2 1
3 -1 3 -2 3 -3
1 + 2 + 1 = . 55
3 9 27
Thus, (0.121) = (0.55) 10
3
(d) The given mixed number (46.78) has a (d) (46.78) EH$ {_{lV g§»`m h¡ Ÿ& BgH$m Xe_bd
9
9
base 9. The Decimal value of the number is: _mZ Bg àH$ma h¡ …
-1
0

1
4 × 9 + 6 × 9 + 7 × 9 + 8 × 9 -2
7 8
36 + 6+ + = 42.86
9 81
Thus, (46.78) = (42.86) 10
9
3.7 Binary to Octal and Hexadeci- 3.7 ~mBZar go Am°ŠQ>b d hoŠgmS>o{g_b _|
mal Conversion and Vice-versa n[adV©Z VWm {dnarV
We have seen the procedure to convert any A^r VH$ h_Zo {H$gr Xe_bd g§»`m H$mo {H$gr AÝ`
given number into decimal. At the same time, nÕ{V _| ~XbZm d BgH$m CëQ>m H$aZm grIm Ÿ& bo{H$Z h_|
we can convert a decimal number into any other
base. In both the cases, one of the numbers EH$ g§»`m H$mo Xygar g§»`m _| n[adV©Z H$aZm h¡ Am¡a XmoZm|