converting a Binary to Decimal number would be:
| Decimal Digit Value |
256 |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
| Binary Digit Value |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
By adding together ALL the decimal number values from right to left at the positions that are represented by a “1” gives us: (256) + (64) + (32) + (4) + (1) = 35710 or three hundred and fifty seven as a decimal number.
Then, we can convert binary to decimal by finding the decimal equivalent of the binary array of digits 1011001012 and expanding the binary digits into a series with a base of 2 giving an equivalent of 35710 in decimal or denary.
Note that in number conversion systems “subscripts” are used to indicate the relevant base numbering system, 10012 = 910. If no subscript is used after a number, then it is generally assumed to be decimal.
Repeated Division-by-2 Method
We have seen above how to convert binary to decimal numbers, but how do we convert a decimal number into a binary number. An easy method of converting decimal to binary number equivalents is to write down the decimal number and to continually divide-by-2 (two) to give a result and a remainder of either a “1” or a “0” until the final result equals zero.
So for example. Convert the decimal number 29410 into its binary number equivalent.
| Number |
294 |
|
Dividing each decimal number by “2” as shown will give a result plus a remainder.
If the decimal number being divided is even then the result will be whole and the remainder will be equal to “0”. If the decimal number is odd then the result will not divide completely and the remainder will be a “1”.
The binary result is obtained by placing all the remainders in order with the least significant bit (LSB) being at the top and the most significant bit (MSB) being at the bottom.
|
| divide by 2 |
| result |
147 |
remainder |
0 (LSB) |
| divide by 2 |
| result |
73 |
remainder |
1 |
| divide by 2 |
| result |
36 |
remainder |
1 |
| divide by 2 |
| result |
18 |
remainder |
0 |
| divide by 2 |
| result |
9 |
remainder |
0 |
| divide by 2 |
| result |
4 |
remainder |
1 |
| divide by 2 |
| result |
2 |
remainder |
0 |
| divide by 2 |
| result |
1 |
remainder |
0 |
| divide by 2 |
| result |
0 |
remainder |
1 (MSB) |
This divide-by-2 decimal to binary conversion technique gives the decimal number 29410 an equivalent of 1001001102 in binary, reading from right to left. This divide-by-2 method will also work for conversion to other number bases.
Then we can see that the main characteristics of a Binary Numbering System is that each “binary digit” or “bit” has a value of either “1” or “0” with each bit having a weight or value double that of its previous bit starting from the lowest or least significant bit (LSB) and this is called the “sum-of-weights” method.
So we can convert a decimal number into a binary number either by using the sum-of-weights method or by using the repeated division-by-2 method, and convert binary to decimal by finding its sum-of-weights.
Gaurav Seth 4 years, 1 month ago
converting a Binary to Decimal number would be:
By adding together ALL the decimal number values from right to left at the positions that are represented by a “1” gives us: (256) + (64) + (32) + (4) + (1) = 35710 or three hundred and fifty seven as a decimal number.
Then, we can convert binary to decimal by finding the decimal equivalent of the binary array of digits 1011001012 and expanding the binary digits into a series with a base of 2 giving an equivalent of 35710 in decimal or denary.
Note that in number conversion systems “subscripts” are used to indicate the relevant base numbering system, 10012 = 910. If no subscript is used after a number, then it is generally assumed to be decimal.
Repeated Division-by-2 Method
We have seen above how to convert binary to decimal numbers, but how do we convert a decimal number into a binary number. An easy method of converting decimal to binary number equivalents is to write down the decimal number and to continually divide-by-2 (two) to give a result and a remainder of either a “1” or a “0” until the final result equals zero.
So for example. Convert the decimal number 29410 into its binary number equivalent.
Dividing each decimal number by “2” as shown will give a result plus a remainder.
If the decimal number being divided is even then the result will be whole and the remainder will be equal to “0”. If the decimal number is odd then the result will not divide completely and the remainder will be a “1”.
The binary result is obtained by placing all the remainders in order with the least significant bit (LSB) being at the top and the most significant bit (MSB) being at the bottom.
This divide-by-2 decimal to binary conversion technique gives the decimal number 29410 an equivalent of 1001001102 in binary, reading from right to left. This divide-by-2 method will also work for conversion to other number bases.
Then we can see that the main characteristics of a Binary Numbering System is that each “binary digit” or “bit” has a value of either “1” or “0” with each bit having a weight or value double that of its previous bit starting from the lowest or least significant bit (LSB) and this is called the “sum-of-weights” method.
So we can convert a decimal number into a binary number either by using the sum-of-weights method or by using the repeated division-by-2 method, and convert binary to decimal by finding its sum-of-weights.
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