Like base ten numbers, we can determine the value of a base two number by placing each digit in its respective place value, then writing its expanded notation.
Example:
Find the value of each of the following binary numbers, giving the values in decimal numbers:
a)1012
b)10112
c)101012
Solution:
a)
24 | 23 | 22 | 21 | 20 |
1 | 0 | 1 |
24 | 23 | 22 | 21 | 20 |
1 | 0 | 1 | 1 |
24 | 23 | 22 | 21 | 20 |
1 | 0 | 1 | 0 | 1 |
We can convert a decimal number into a binary number by repeatedly dividing the base ten number by two. Then, write the remainders from the bottom to the top as the answer:
Example:
Write each of the following base ten numbers as a binary number:
a)510
b)7810
Solution:
a)510 = 1012
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