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

16 Chapter 1 Review of algebraic techniques
Example1.18 Convert 14397 tohexadecimal.
Solution We divide repeatedly by 16, noting the remainder.
Remainder
14397÷16=899r13 13
899÷16= 56r3 3
56÷16= 3r8 8
3÷16= 0r3 3
Recall that 13 inhexadecimal isD.Reading up the Remainder column wehave
as before.
14397 10
= 383D 16
Electronic engineers need to be familiar with the decimal, binary and hexadecimal systemsandbeabletoconvertbetweenthem.Theequivalentrepresentationsofthedecimal
numbers 0--15 are provided inTable 1.4.
Table1.4
Decimal Binary Hex Decimal Binary Hex
0 0000 0 8 1000 8
1 0001 1 9 1001 9
2 0010 2 10 1010 A
3 0011 3 11 1011 B
4 0100 4 12 1100 C
5 0101 5 13 1101 D
6 0110 6 14 1110 E
7 0111 7 15 1111 F
Convertingfrombinarytohexadecimal
There is a straightforward way of converting a binary number into a hexadecimal number.Thedigitsofthebinarynumberaregroupedintofours,orquartets,(fromtherighthand
side) and each quartetisconverted toits hex equivalent using Table 1.4.
Example1.19 Convert 1101011100111 2
into hexadecimal.
Solution Working from the right, the binary number is grouped into fours, with additional zeros
being added as necessary tothe final grouping.
0001 1010 1110 0111