Math Help ( Not Cheating).?

Question

Okay, in a computer class we are learning bianary, and how to convert it and stuff.

The teacher says he wants to see some work but that you can use a calculator.

The problem for those of you who do not know is the whole point of the thing is to get the remainders in division.

So is there anyway to get a remainder using a calculator or to calculate it using the decimals?

I have a TI-83 Plus.

Or do I just have to divide it all by hand?

Answer 1

If you divide 86/5 on a calculator, you get 17.2.
Subtract the 17 (the part in front of the decimal), and you are left with 0.2 (the part after the decimal).
Multiply this by what you divided by (5) and you will get 1.
This is the remainder.
So 86/5 = 17 remainder 1.

The same method applies with any other numbers.

Answer 2

Suppose you are dividing 17 by 6. The calculator will display 2.83333333 . . .. The part after the decimal represents the remainder. Subtract the part in front of the decimal (the 2), and get 0.83333333 . . .. Then multiply by 6 (the divisor) and the answer is 5, which is the remainder.
So 17/6 = 2 r 5

Another example:
129/7 = 18.428571 . . .
0.428571 . . . * 7 = 3
So 129/7 = 18 r 3

Answer 3

The beauty of binary is it's simplicity of representation.
In decimal the positions are: 1, 10, 100, 1000, etc.
For binary they are: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, etc.
So you can do conversion by subtraction alone.
e.g. let's convert a number larger than 256 but less than 512.
Say 356 in decimal, so we'll have a 256 bit, subtract that.
It leaves 100, too much for 128 bit, so it's 0, we have a 64 bit.
Subtract 64, to leave 36, so we have a 32 bit, leaving 4.
No 16 or 8, so 356 decimal is 101100100 in binary.

Answer 4

Yes you can use a calculator.

Example:
What is the remainder of 673 divided by 6

673/6 = 112.1667
Round down to 112...
112 * 6 = 672
673 - 672 = 1
So the remainder of 673 divided by 6 is 1.

So in general, if you are looking for R when you do a/b:
a/b = c
floor(c) * b = a + R

Also, if you use the calculator on your computer, you can use the MOD function (you will have to be in "Scientific" mode).
Just do 673 MOD 6 and you will get 1, since MOD returns the remainder of integer division.