In order to convert binary numbers to decimals you must start from the end and multiply where there is a 1 by an exponent of 2. For the number 110010101 for example:
2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0=
1 1 0 0 1 0 1 0 1
256 + 128 + 0 + 0 + 16 + 0 + 4 + 0 + 1 = 405
So the answer is 405.
Converting decimals to binary is similar, but not the same. In order to do this, u must divide your starting number by two, recording if there is a remainder or not as a 1 or a 0 until you divide all the way through the number. For the number 529 for example:
(529/2) (264/2) (132/2) (66/2) (33/2) (16/2) (8/2) (4/2) (2/2) (1/2)
(264 R. 1) (132) (66) ( 33) (16 R. 1) (8) (4) (2) (1) (0 R. 1)
1 0 0 0 1 0 0 0 0 1
So the answer is 1000010001.
Positional vs. Non- Positional
Positional and Non-Positional number systems are very simple to understand. A positional number system consists of numbers where each position is related to the next by a constant multiplier. A non-positional number system does not have a constant multiplier for each position. Rather, in a non-positional number system, the numbers are represented as symbols to convey their purpose. For example, writing numbers in roman numerals is a specific way to write using a non-positional numbering system.
2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0=
1 1 0 0 1 0 1 0 1
256 + 128 + 0 + 0 + 16 + 0 + 4 + 0 + 1 = 405
So the answer is 405.
Converting decimals to binary is similar, but not the same. In order to do this, u must divide your starting number by two, recording if there is a remainder or not as a 1 or a 0 until you divide all the way through the number. For the number 529 for example:
(529/2) (264/2) (132/2) (66/2) (33/2) (16/2) (8/2) (4/2) (2/2) (1/2)
(264 R. 1) (132) (66) ( 33) (16 R. 1) (8) (4) (2) (1) (0 R. 1)
1 0 0 0 1 0 0 0 0 1
So the answer is 1000010001.
Positional vs. Non- Positional
Positional and Non-Positional number systems are very simple to understand. A positional number system consists of numbers where each position is related to the next by a constant multiplier. A non-positional number system does not have a constant multiplier for each position. Rather, in a non-positional number system, the numbers are represented as symbols to convey their purpose. For example, writing numbers in roman numerals is a specific way to write using a non-positional numbering system.
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