answer
10101001101.11010110
steps
1. To convert a whole number to binary, you divide the number by 2 over and over.
2. Each time you divide, you write down the remainder (the left over amount).
3. The remainders become the binary digits, starting from the bottom.
4. For example, 673 divided by 2 is 336 remainder 1.
5. 336 divided by 2 is 168 remainder 0.
6. You keep dividing by 2 until you reach 0.
7. The remainders are 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1.
8. So 673 in binary is 10101001101.
9. To convert a decimal to binary, you multiply by 2 over and over.
10. You write down the whole number part each time.
11. For 0.23, 0.23 x 2 is 0.46. The whole number part is 0.
12. 0.46 x 2 is 0.92. The whole number part is 0.
13. You keep going until you reach 0.
14. The whole number parts are 0, 0, 1, 1, 1, 0, 1, 0, 1, 1.
15. So 0.23 in binary is 0.11010110.
16. Putting it together, 673.23 in binary is 10101001101.11010110.
1. The whole number part 673 can be converted directly into binary by repeatedly dividing by 2 and recording the remainders.
673 / 2 = 336 remainder 1
336 / 2 = 168 remainder 0
168 / 2 = 84 remainder 0
84 / 2 = 42 remainder 0
42 / 2 = 21 remainder 0
21 / 2 = 10 remainder 1
10 / 2 = 5 remainder 0
5 / 2 = 2 remainder 1
2 / 2 = 1 remainder 0
1 / 2 = 0 remainder 1
So the whole number part 673 in binary is 10101001101
2. To convert the fractional part 0.23 into binary, we multiply it by 2 and record the whole number part of the result, repeating this process until we get 0.
0.23 x 2 = 0.46 -> 0
0.46 x 2 = 0.92 -> 0
0.92 x 2 = 1.84 -> 1
0.84 x 2 = 1.68 -> 1
0.68 x 2 = 1.36 -> 1
0.36 x 2 = 0.72 -> 0
0.72 x 2 = 1.44 -> 1
0.44 x 2 = 0.88 -> 0
So the fractional part 0.23 in binary is 0.11010110
Putting the whole number and fractional parts together:
673.23 in binary is 10101001101.11010110
Therefore, 673.23 converted to binary is 10101001101.11010110
claudeAI