Final answer:
To determine the number of binary digits from an integer with 100 octal digits, we multiply the number of octal digits by 3, as each octal digit is represented by three binary digits, resulting in 300 binary digits.
Step-by-step explanation:
The question asks how many binary digits a positive integer with 100 octal digits will have. To solve this, we need to understand the relationship between octal and binary numbers. Octal numbers are based on the base-8 number system, while binary numbers are based on the base-2 number system. Each octal digit can be directly converted into a three-digit binary number. For instance, the octal digit '7' equals to '111' in binary, while '1' in octal equals '001' in binary.
To convert a number from octal to binary, we replace each octal digit with its corresponding three-digit binary equivalent. So, if an integer has 100 digits in octal, it will have 100 x 3 = 300 binary digits, as there are three binary digits for each octal digit. This method is reliable because it falls back on the basics of how numerical systems are constructed, similar to how integer powers work, like 10³ which is 1,000, or 10⁻⁴ which is 0.0001.
When counting digits across different numeral systems, it is essential to understand the exponent representation and how to convert numbers from one base to another. Just as how we can break complex numbers into simpler units of ten for handling scientific notation, we can also break an octal number into units of binary digits that are based on powers of two. In the case of the number 1,372,568, moving the decimal six places in scientific notation parallels converting each isonumeric place of an octal number into a set of binary numbers.