Sets and Logics, problem to solve a question

[NightFire]

Homework Statement

Convert (AC3)16 to base 10.

I'm new to this kind of material. I would really appreciate your help for this one.
Thanks,
Roy

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi Roy!

Hint: what is (A00)16 to base 10 ?

 

[eumyang]

See http://www.permadi.com/tutorial/numHexToDec/index.html" and try it yourself. Remember that:
the hexadecimal digit A corresponds to the decimal number 10,
the hexadecimal digit B corresponds to the decimal number 11,
...
the hexadecimal digit F corresponds to the decimal number 15.

 

[NightFire]

so basically its: (10123)16 ?? did i convert it correctly?

 

[eumyang]

No, it's not. Did you read the website that I linked in my previous post?
(http://www.permadi.com/tutorial/numHexToDec/index.html")

 

[NightFire]

hi roy!

Hint: What is (a00)16 to base 10 ?

(1010100)10 ?

 

[Zach Knight]

Consider the number 152 in base 10. Another way to write this number is 2*10⁰+5*10¹+1*10².
If we change the base, we just change all of those tens. For example
152(base 8)=2*8⁰+5*8¹+1*8²=2+40+64=106(base 10)
Can you write AC3(base 16) in the form above?

 

[NightFire]

Consider the number 152 in base 10. Another way to write this number is 2*10⁰+5*10¹+1*10².
If we change the base, we just change all of those tens. For example
152(base 8)=2*8⁰+5*8¹+1*8²=2+40+64=106(base 10)
Can you write AC3(base 16) in the form above?

i see.
so basically i can write it this way?? : (AC3)16 = (10123)10
3*10^0 + 2*10^1 + 1*10^2 + 0*10^3 + 1*10^4 ?

Thanks

 

[NightFire]

Somebody?! :(

 

[SW VandeCarr]

i see.
so basically i can write it this way?? : (AC3)16 = (10123)10
3*10^0 + 2*10^1 + 1*10^2 + 0*10^3 + 1*10^4 ?

Thanks

In base 16, A=10 C=12 so 10(16^2) + 12(16) + 3 = 2560 + 192 + 3 = 2755 b10 = AC3 b16

What would FF be in base 10?

 

[NightFire]

in base 16, a=10 c=12 so 10(16^2) + 12(16) + 3 = 2560 + 192 + 3 = 2755 b10 = ac3 b16

what would ff be in base 10?

10(10^2) + 12(10) + 3 = 1000+120+3= 1123

??

 

[SW VandeCarr]

10(10^2) + 12(10) + 3 = 1000+120+3= 1123

??

You are wrongly multiplying on a base of 10. AC3 is a base 16 number so 16 is your base for conversion to base 10. 10 b16 = 16 b10; 100 b16= 16^2 = 256 b10; FF b16 = 255 b10. The base 16 "digits" are 0 1 2 3 4 5 6 7 8 9 A B C D E F. You are probably confused (as many are) because the same notation is used for the first ten digits (including zero). It would probably be better if we made up all new digits for different bases, but that's not the case. So 99 b16 = 9(16) + 9 = 144+9 = 153 b10. Nine (9) is not the highest digit in base 16.