Question

two schools are merging and to adapt to the increased size of the student body, the school is changing its system for keeping track of all student ids from a system that uses 4-bit binary numbers to one that uses 8-bit binary numbers (aka 1 byte). which of the following best describes what effect this change will have? a. the 8-bit system will be able to represent twice as many values as the 4-bit system. b. the 8-bit system will be able to represent sixteen times as many values as the 4-bit system. c. the 8-bit system will be able to represent eight times as many values as the 4-bit system. d. the 8-bit system will be able to represent the same number of values as the 4-bit system, it will just include more zeros. submit

Answer 1

Explanation:

Answer 2

The 8-bit system can represent sixteen times as many values as the 4-bit system because 256 is sixteen times larger than 16. Each bit in a binary number doubles the number of representable values.

Step-by-step explanation:

When a school system upgrades from a 4-bit binary number system to an 8-bit binary number system, the number of unique values that can be represented increases significantly. In binary, each bit represents a power of 2, so a 4-bit system can represent
`2^4` or 16 different values. An 8-bit system, however, can represent
`2^8` or 256 different values.

Therefore, the correct answer to the question is a. the 8-bit system will be able to represent sixteen times as many values as the 4-bit system. This is because 256 (the number of values in an 8-bit system) is sixteen times greater than 16 (the number of values in a 4-bit system).

The basic unit of computer memory is the byte, which is equivalent to 8 bits. The unit for one million bytes is a megabyte.