Long answer questions:

1. How can you determine the value of a digit in a number system?

2. What are the characteristics of the octal number system?

3. Write the steps to convert a decimal number to a binary number.

To determine a digit's value in a number system, multiply it by the base raised to its positional power. The octal number system is base-8, using digits 0-7, and is important in computing. To convert a decimal number to binary, keep dividing by 2 and recording remainders, then read them in reverse order.
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Answered by Anonymous | 2025-07-04

How can you determine the value of a digit in a number system?
In any number system, the value of a digit is determined by both the digit itself and its position within the number. This is often referred to as 'place value.' For example, in the decimal system (base 10), the number 234 can be broken down as follows:

The digit '2' is in the hundreds place, so its value is 2 × 1 0 2 = 200 .
The digit '3' is in the tens place, so its value is 3 × 1 0 1 = 30 .
The digit '4' is in the ones place, so its value is 4 × 1 0 0 = 4 .

Similarly, in other number systems, the base changes. For example, in binary (base 2), octal (base 8), or hexadecimal (base 16), the position of each digit still determines its value with the respect to the base.

What are the characteristics of octal number system?
The octal number system is a base-8 number system that uses digits from 0 to 7. Here are the key characteristics:

Base: 8
Digits Used: 0, 1, 2, 3, 4, 5, 6, 7
Positional Value: Each digit's value depends on its position, with each position representing a power of 8. For instance, in the octal number 345:
The digit '3' is in the "64s" place ( 3 × 8 2 ),
The digit '4' is in the "8s" place ( 4 × 8 1 ),
The digit '5' is in the "1s" place ( 5 × 8 0 ).


Applications: Often used in digital electronics and computing since each octal digit corresponds to exactly three binary digits (bits).


Write the steps to convert a decimal number to a binary number.
To convert a decimal number to a binary number, follow these steps:

Step 1: Start with the decimal number you wish to convert.
Step 2: Divide the number by 2, noting the quotient and the remainder.
Step 3: The remainder is the least significant bit (rightmost bit) in the binary number.
Step 4: Use the quotient from the previous division as the new number and repeat the process until the quotient is 0.
Step 5: The binary number is read from the bottom to the top, using the remainders.

Example: Convert 13 to binary.

13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1

Reading from bottom to top, the binary representation of 13 is 1101.

Answered by MasonWilliamTurner | 2025-07-06