Question:
Conversions - Binary, Octal, Hexadecimal to DECIMAL? with examples.?
WaleedBinAbdulMaalik
2013-02-23 23:21:50 UTC
Conversions:
Binary to Decimal,
Octal to Decimal
Hexadecimal to Decimal.
Three answers:
Naitik Kundalia
2013-02-23 23:36:37 UTC
Any number system has a base.



Decimal = Base 10 i.e. the "ones" place consists of 10^0 power. while the tens place is 10^1



Octal then = Base 8 i.e. the "ones" place consists of 8^0 (0-7) and the tens (eights) place is 8^(1)



Hex = Base 16 the "ones" place consists of 16^0 and the tens (sixteens) place is 16^(1)

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Binary to Decimal :-



Binary :-10001011



Decimal is :-1(2^7)+0(2^6)+0(2^5)+0(2^4)+1(2^3)+0(2^2)+1(2^1)+1(2^0)

1(128)+0+0+0+1(8)+0+1(2)+1(1)

128+8+2+1

139



Octal:-213



Decimal is :-2(8^2)+1(8^1)+3(8^0)

2(64)+1(8)+3(1)

128+8+3

139

Hexa-Decimal :-8B



Decimal is :- 8(16^1)+B(16^0)

8(16)+11(1)

128+11

139

In hexadecimal there is 16 digits 0 to 15 but digits are always singals so there is numbers 0 to 9 and

then comes 10 but 10 has 2digits so 10 becomes A then 11 becomes B 12 becomes C 13 becomes D 14 becomes E and 15 becomes F.



So hexa decimal has 16 numbers :-0 TO 9,A,B,C,D,E,F.
Fred
2013-02-23 23:30:15 UTC
Well, considering you are asking a very expansive question, I am going to give you a general answer:



Any number system has a base.



Decimal = Base 10 i.e. the "ones" place consists of 10^0 power. while the tens place is 10^1



Octal then = Base 8 i.e. the "ones" place consists of 8^0 (0-7) and the tens (eights) place is 8^(1)



Hex = Base 16 the "ones" place consists of 16^0 and the tens (sixteens) place is 16^(1)



Given this knowledge, you simply extract the largest multiple power of eight: so for example,



100: the largest power of eight is equal to 64: You have 1 8^2: Now 100 - 64 equals 36. repeat the process: The largest power of eight is 1, and you have 4 of them. 36 - 32 = 4. Which is your one's place value.



1 4 4

8^2 (place) 8^1 8^0
peagler
2016-08-08 08:29:45 UTC
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