The decimal system is based on the number ten (base 10)
There are ten digits (0 to 9).
The value of each place is found by starting on the right with the ONES place
and multiplying by ten to get each place after that: ones, ten, hundred, thousand,
ten thousand, etc.
The number 47 has a 7 in the ones place and a four in the tens place.
Its value is equal to 4 times 10 plus 7 times 1 or 4*10 + 7*1.
The number 407 has a four in the hundreds place, a zero in the tens place and
7 in the ones place.
Its value is equal to 4*100 + 0*10 + 7*1.
We could shorten this to just 4*100 + 7*1 since multiplying by zero will always
give us zero.
The memory of a computer is comprised of BITS (BInary digiTS).
A bit can have one of two values.
We can think of these two values as ON / OFF, True / False, or 0/1.
Usually, several bits are grouped together to represent numbers.
Because each bit can have just one of two values, the binary (base 2) numbering
system is perfect for computers.
There are two digits \: 0 and 1.
The value of each place is found by starting on the right with the ones place
and then multiplying by TWO to get each place.
The places in the binary number system (starting on the right) are
one, two, four, eight, sixteen, thirty two, sixty four, one hundred twenty-eight,
two hundred and fifty six, etc.
256 128 64 32 16 8 4 2 1
The value of a number is found just like in the decimal numbering system: multiply
the value of the digit by the place value.
The binary number 101 has a one in the ones place, a zero in the twos place
and a one in the fours place:
4 2 1
1 0 1
Its value is 1*1 + 0*2 + 1*4. We can simplify this by just adding together the
places with a one in them 1+4.
The binary number 101 is equivalent the decimal number 5.
Try to evaluate each number then move the mouse over the answer button to see if you are right. If your are stuck, you can move the mouse over each bit to see its place value.