Page 144 - FUNDAMENTALS OF COMPUTER

144 Fundamentals of Computers NPP

Here, digits '0' to '9' have the same meaning `hm§ na 0 go 9 Ho$ AW© dhr h¢ Omo {H$ Xe_bd
as in decimal number system. The digit A g§»`m nÕ{V _| h¢ Ÿ& bo{H$Z ‘A’ H$m _mZ Xe_bd Ho$ ‘10’
represents decimal 10 and F represents decimal Ho$ ~am~a hmoVm h¡ Ÿ& ‘B H$m 11 Ho$ VWm Bgr Vah F H$m
15. Note that A, B, C, D, E, F, are taken from _mZ ‘15’ Ho$ ~am~a hmoVm h¡ Ÿ& hmbm§{H$ A,B, C, D, E, F
English Alphabets but here they represent A§J«oOr Ho$ Ajam| go {bE JE h¢ Ÿbo{H$Z `hm± na `o g§Ho$V
numbers. It is very useful to remember 4-bit binary A§H$ h¡ Ÿ& H$B© ñWmZm| na hoŠgmS>o{g_b A§H$m| Ho$ 4-{~Q> _|
equivalent of the Hexadecimal digits: ~mBZar Vwë`m§H$m| H$m H$m_ n‹S>Vm h¡ Ÿ& Bgr{bE Vm{cH$m
3.3 H$mo AÀN>r Vah `mX H$a boZm Mm{hE Ÿ&
Table 3.3
Decimal Hex. 4 bit Decimal Hex. 4 bit.
Digit Binary Digit Binary
0 0 0000 8 8 1000
1 1 0001 9 9 1001
2 2 0010 10 A 1010
3 3 0011 11 B 1011
0100
4 4 NPP 12 C 1100
5 5 0101 13 D 1101
6 6 0110 14 D 1110
7 7 0111 15 F 1111
The Counting sequence can also be hoŠgmS>o{g_b _| g§»`mAm| H$s JUZm g_mZ {gÕm§V
generated using the same principle. Increment H$m Cn`moJ H$aVo hþE H$s Om gH$Vr h¡ Ÿ& A§H$m| H$mo grYo
the digits until you reach at the greatest hmW H$s Va\$ go ~‹T>mZm ewê$ H$a| Ÿ& O¡go hr g~go ~‹S>m
digit. Now, reset this digit to smallest and A§H$ AmE, CgHo$ ~mX g~go N>moQ>m A§H$ {bI X| VWm EH$
take a carry. Thus, first few numbers of
Hexadecimal number system can be written hm{gb H$m b| Ÿ& Bg Vah go hoŠgmS>o{g_b g§»`m nÕ{V
as: _| àW_ Hw$N> g§»`mE± Bg Vah go àmá H$s Om gH$Vr h¢…
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2A, 2B

Problem 3.4 àíZ 3.4
What will be the next Hexadecimal to the ZrMo {bIo hoŠgmS>o{g_b g§»`m hoVw AJbr g§»`m
following hexadecimal numbers. àmßV H$amo …

(1) 20 (2) 39 (3) FF (4) 10F
Solution: hc:
(1) 20 → 21 (2) 39 → 3A (3) FF → 100 (4) 10F → 110