ACMS 40390: Fall 2010
Numerical Analysis
| First test review | Monday, 09/27 | in class |
|---|---|---|
| First in class test | Wednesday, 09/29 | in class |
| Second test review | Monday, 10/25 | in class |
| Second in class test | Wednesday, 10/27 | in class |
| Final test review | TBA | TBA |
| Final test | TBA | TBA |
In the decimal system, we use the digits 0-9 to represent numbers, and things are organized into columns. Take the decimal number 285 for example:
H | T | O
2 | 8 | 5
such that "H" is the hundreds column, "T" is the tens column, and "O" is the ones column. So the decimal number "285" is 2-hundreds plus 8-tens plus 5-ones.
The ones column stands 10^0, the tens column stands 10^1, the hundreds column stands 10^2 and so on, so
10^2|10^1|10^0
2 | 8 | 5
the number 285 is really {(2*10^2)+(8*10^1)+(5*10^0)}.
The binary system works under the exact same way as the decimal system, except it operates in the base 2 rather than the base 10. In other words, instead of columns being
10^2|10^1|10^0
they are
2^2|2^1|2^0
Instead of using the digits 0-9, we only use 0-1 digits.
Examples:
What will the binary number 1011 be in the decimal system?
Answer: By using the columns, we have
2^3|2^2|2^1|2^0
1 | 0 | 1 | 1
Therefore
1011=(1*2^3)+(0*2^2)+(1*2^1)+(1*2^0)
= (1*8) + (0*4) + (1*2) + (1*1)
= 11 (in decimal system)