Question

List out first 10 decimal equivalent numbers in binary, octal
hexadecimal number systems.

Answer 1

The first ten decimal numbers are listed alongside their equivalent in binary, octal, and hexadecimal number systems. Understanding these equivalents is important for tasks such as programming where different number systems are often used.

Step-by-step explanation:

When comparing numbers across different number systems, it can be helpful to understand their decimal equivalents. This is particularly important when considering binary, octal, and hexadecimal systems, which are common in fields like computer science. Here, we'll list the first ten decimal numbers and their equivalent in binary, octal, and hexadecimal.

• Decimal 0 = Binary 0, Octal 0, Hexadecimal 0
• Decimal 1 = Binary 1, Octal 1, Hexadecimal 1
• Decimal 2 = Binary 10, Octal 2, Hexadecimal 2
• Decimal 3 = Binary 11, Octal 3, Hexadecimal 3
• Decimal 4 = Binary 100, Octal 4, Hexadecimal 4
• Decimal 5 = Binary 101, Octal 5, Hexadecimal 5
• Decimal 6 = Binary 110, Octal 6, Hexadecimal 6
• Decimal 7 = Binary 111, Octal 7, Hexadecimal 7
• Decimal 8 = Binary 1000, Octal 10, Hexadecimal 8
• Decimal 9 = Binary 1001, Octal 11, Hexadecimal 9
• Decimal 10 = Binary 1010, Octal 12, Hexadecimal A

Understanding these equivalents is crucial for tasks such as programming, where various number systems are used, and calculations might involve subtraction of exponentials or multiplying by powers of ten. For example, multiplying by a power of ten involves shifting the decimal point to the right, as in 10³ (10 to the power of 3), which equals 1000. Conversely, dividing by powers of ten involves shifting the decimal point to the left.

Answer 2

Explanation:Base 10 (Decimal) — Represent any number using 10 digits [0–9]

Base 2 (Binary) — Represent any number using 2 digits [0–1]

Base 8 (Octal) — Represent any number using 8 digits [0–7]

Base 16(Hexadecimal) — Represent any number using 10 digits and 6 characters [0–9, A, B, C, D, E, F]

In any of the number systems mentioned above, zero is very important as a place-holding value. Take the number 1005. How do we write that number so that we know that there are no tens and hundreds in the number? We can’t write it as 15 because that’s a different number and how do we write a million (1,000,000) or a billion (1,000,000,000) without zeros? Do you realize it’s significance?

First, we will see how the decimal number system is been built, and then we will use the same rules on the other number systems as well.

So how do we build a number system?

We all know how to write numbers up to 9, don’t we? What then? Well, it’s simple really. When you have used up all of your symbols, what you do is,

you add another digit to the left and make the right digit 0.

Then again go up to until you finish up all your symbols on the right side and when you hit the last symbol increase the digit on the left by 1.

When you used up all the symbols on both the right and left digit, then make both of them 0 and add another 1 to the left and it goes on and on like that.

If you use the above 3 rules on a decimal system,

Write numbers 0–9.

Once you reach 9, make rightmost digit 0 and add 1 to the left which means 10.

Then on right digit, we go up until 9 and when we reach 19 we use 0 on the right digit and add 1 to the left, so we get 20.

Likewise, when we reach 99, we use 0s in both of these digits’ places and add 1 to the left which gives us 100.

So you see when we have ten different symbols, when we add digits to the left side of a number, each position is going to worth 10 times more than it’s previous one.