Base 10 conversion (Java) I need help!

What is the value of the binary number 01000001 in base 10?

The answer is 65. But I need help on how it is 65... I am really lost, I am terrible at math. Can anyone explain this easy for me?

All help appreciated.

 0      1      0      0      0      0     0      1
*2^7   *2^6   *2^5   *2^4   *2^3   *2^2  *2^1   *2^0
= 0    = 64   = 0    = 0    = 0    = 0    = 0    = 1

62 + 1 = 64

The right most position is 1 * 2^0; for each position left, you increment the power and multiply by a 1 or 0, depending on whatever digit is in that position.

Edited by groovicus, 30 January 2011 - 04:59 PM.

Start with 1 on the right hand side: 1
Multiply it by 2, put that to the left: 2 1
Multiply that next value by 2: 4 2 1
And so on until you have 8 numbers.
128 64 32 16 8 4 2 1

These are the values that are implied by a 1 in a given location in binary.

Then you simply add up the values.

01000001

is 0*128 + 1*64 + 0*32 + 0*16 + 0*8 + 0*4 +0*2 + 1*1
64 + 1 = 65

11111111

is 255, 128 + 64 + 32 + 16 + 8 + 4 + 2 +1

00000000

is just 0



It takes getting used to. The best way in my opinion (and that of my mathematics teacher) is to just get some numbers and practice. For example what are the following in binary

1
2
5
10
25

and the following in decimal.

10101010
01010101
00100100
00000111

Edited by JosiahK, 30 January 2011 - 04:54 PM.

Thanks to both of you. I understand this a lot clearer!