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NPP

NPP Number System, Boolean Algebra and Logic Circuits 143

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23 , 24, 25, 26, 27, 30 .............
Problem 3.1 àíZ 3.1
Write first fifty numbers of octal number Am°ŠQ>b g§»`m nÕ{V H$s àW_ nMmg g§»`mE§ {bImo&
system.
Solution: hc:
Following are first fifty numbers of octal {ZåZ àW_ 50 Am°ŠQ>c H$s g§»`mE± h¢
number system :
0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32,
33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61
Problem 3.2 àíZ 3.2
In the above problem what are the octal Cnamoº$ g_ñ`m _| ZrMo Xem©E Xe_bd g§»`mAm| Ho$
equivalents for the following decimal numbers: {bE Am°ŠQ>b àmßV H$amo:

(a) 6 (b) 9 (c) 35 (d) 49 (e) 16
Solution: hc:
'0' is equivalent to '0' and so on, 6 is "0" Vwë` h¡ "0" Ho$ VWm Bgr Vah EH$-EH$ ~‹T>mVo
equivalent to 6, the following results are OmE± Ÿ& "6" Vwë` hmoJm "6" Ho$ Am¡a Bgr Vah ZrMo {bIo
obtained:
n[aUm_ àmßV hm|Jo …

(a) ( ) 6 10 → ( ) 6 (b) ( ) 9 10 → ( ) 8 (c) ( ) → ( ) (d) ( ) → ( ) 8
11
49
43
61
35
10
8
8
10
16
20
(e) ( ) → ( ) 8
10
Problem 3.3 àíZ 3.3
In problem 3.1 what are the decimal g_ñ`m 3.1 _| {ZåZ{b{IV Am°ŠQ>b g§»`mAm| Ho$
equivalents for the following octal numbers: {bE Xe_bd g§»`m àmßV H$amo-
(a) 5 (b) 13 (c) 54
Solution : hc:
Take help of the table start with '0' which Vm{cH$m H$s ghm`Vm go h_ ~Vm gH$Vo h¢ {H$
is equivalent to '0', you will find the solution.
(a) ( ) 5 → ( ) 5 10 (b) ( ) → ( ) 10 (c) ( ) → ( ) 10
11
44
54
13
8
8
8
3.4 Hexadecimal Number System 3.4 hoŠgmS>o{g_b g§»`m nÕ{V
The Hexadecimal Number system has Bg g§»`m nÕ{V _| 16 {d{^ÝZ g§Ho$Vm| H$m Cn`moJ
sixteen distinct symbols used as digits. hmoVm h¡, {OÝh| h_ hoŠgmS>o{g_b A§H$ H$hVo h¢ Ÿ& Bgr{bE
Therefore base of this number system is 16. The
following Hexadecimal digits are used for Bg g§»`m nÕ{V H$m AmYma (~og) 16 h¢ Ÿ& hoŠgmS>o{g_b
making the numbers: A§H$ Bg àH$ma h¢ …
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F