082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

1.3 Number bases 15
Example1.16 Convert the following hexadecimal numbers todecimal numbers: (a)93A (b)F9B3
Solution (a) Noting thathexadecimal numbers use base16 we have
93A 16
= 9(16 2 ) +3(16 1 ) +A(16 0 )
= 9(256) +3(16) +10(1)
= 2362 10
(b) F9B3 16
= F(16 3 ) +9(16 2 ) +B(16 1 ) +3(16 0 )
= 15(4096) +9(256) +11(16) +3(1)
= 63923 10
Convertingfromdecimaltohexadecimal
Table 1.3 provides powers of 16 which help in the conversion from decimal to hexadecimal.
Table1.3
16 0 1
16 1 16
16 2 256
16 3 4096
16 4 65536
The following example illustrateshow toconvert from decimal tohexadecimal.
Example1.17 Convert 14397 toahexadecimal number.
Solution We need to express 14397 as the sum of multiples of powers of 16. From Table 1.3 we
see that the highest number that does not exceed 14397 is 4096. We express 14397 as
amultipleof4096withanappropriateremainder. Dividing14397by4096weobtain3
with a remainder of 2109. So we may write
14397 = 3(4096) +2109
Wenowfocuson2109andapplythesameprocessasabove.FromTable1.3thehighest
number thatdoes not exceed 2109 is 256:
2109 = 8(256) +61
Finally, 61 = 3(16) +13. So wehave
14397 = 3(4096) +8(256) +3(16) +13
= 3(16 3 ) +8(16 2 ) +3(16 1 ) +13(16 0 )
FromTable 1.2 wesee that13 10
isDinhexadecimal, sowe have
14397 10
= 383D 16
As with base 2 we can convert decimal numbers by repeated division and noting the
remainder. The previous example isreworked toillustratethis.