Number Systems | MCQs

Explanation

Solution

• 13 ÷ 2 = 6, remainder 1

• 6 ÷ 2 = 3, remainder 0

• 3 ÷ 2 = 1, remainder 1

• 1 ÷ 2 = 0, remainder 1

Reading the remainders from bottom to top: 1101

So, 13 in binary = 1101.

Explanation

A number system that has eight different symbols to represent any quantity is known as Octal.

The Octal number system uses digits from 0 to 7.

It is often used in computing as a simpler alternative to binary representation.

Explanation

To convert the hexadecimal number 1D7F₁₆ to a decimal number, we can break it down as follows:

• 1 in hexadecimal = 1 × (16^3) = 1 × 4096 = 4096
• D in hexadecimal = 13 × (16^2) = 13 × 256 = 3328
• 7 in hexadecimal = 7 × (16^1) = 7 × 16 = 112
• F in hexadecimal = 15 × (16^0) = 15 × 1 = 15

Now, sum these values:

4096 + 3328 + 112 + 15 = 7551

So, the decimal equivalent of 1D7F₁₆ is 7551.

Explanation

Hexadecimal is the name of the numbering system that is base 16