Question

Question :3.3 [10] Convert 5ED4 into a binary number. What makes base 16 (hexadecimal) an attractive numbering system for representing values in computers?

Short answer

The required result will be 0101 1110 1101 0100.

Step-by-step solution

Define the concept.

The hexadecimal number system uses base 16 where the decimal number system uses base 10 and the binary number system uses base 2.

For example, “A” is equivalent to the value of decimal number system “10” and that is also equivalent to the value of binary number system “1010”.

Determine the calculation.

In the hexadecimal number system, 5 is equivalent to the value of the binary number system 0101.

In the hexadecimal number system, E is equivalent to the value of the binary number system 1110.

In the hexadecimal number system, D is equivalent to the value of the binary number system 1101.

In the hexadecimal number system, 4 is equivalent to the value of the binary number system 0100.

Hence, in the hexadecimal number system, 5ED4 is equivalent to the value of the binary number system 0101 1110 1101 0100.

The hexadecimal number system is immensely useful. The modern computer system uses the base 16. Such that is 64 bit, so 16*4. This representation makes the representation more accurate and easier. Hence, this is basically the primary representation of the memory addresses in the computer system. Besides that, it can be able to allow large numbers to be shown in comparatively fewer digits. Such that, the hexadecimal word for 32 bits is represented in the format of "FFFFFFFF" which is in the 8 digits. But the decimal number system is written as 4294967295, which is in the 10 digits.