Computer Number Systems & Binary-to-Decimal Conversion

A set of question-and-answer flashcards covering definitions, characteristics, and conversions of decimal, binary, octal, and hexadecimal number systems, plus worked binary-to-decimal examples from the lecture.

What are the two learning competencies related to computer number systems stated in the lesson?

1) Differentiate the various computer number systems. 2) Apply computer number systems in practical situations.

What is a number system?

A structured way of representing numbers using a consistent set of symbols or digits.

Which number system is known as the Base-10 system and which digits does it use?

The Decimal Number System; it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Which number system is called the Base-2 system and which digits does it use?

The Binary Number System; it uses two digits: 0 and 1.

Why is the binary number system referred to as “machine language”?

Because it is the only language directly understood by computer hardware.

What role does the binary number system play in digital electronics?

It is the basis of all digital electronic hardware for processing and data representation.

How is the uppercase letter “A” represented in binary ASCII code?

01000001

Which number system is Base-8 and what digits does it use?

The Octal Number System; it uses eight digits: 0 through 7.

Which number system is Base-16, what symbols does it use, and why is it efficient?

The Hexadecimal Number System; it uses sixteen symbols (0–9 and A–F) and can express large numbers using fewer digits.

List the four main steps for converting a binary number to its decimal equivalent.

1) Write the binary number from right to left. 2) Assign powers of 2 starting with 2⁰ on the rightmost bit. 3) Multiply each bit by its corresponding power of 2. 4) Add all the results to get the decimal value.

In binary-to-decimal conversion, what is the value of any number raised to the power of zero?

1

What is the decimal equivalent of 1101₂?

13

What is the decimal equivalent of 1010₂?

10

What is the decimal equivalent of 1100₂?

12

What is the decimal equivalent of 10010₂?

18

What is the decimal equivalent of 11101₂?

29

What is the decimal equivalent of 11011₂?

27

What is the decimal equivalent of 10101₂?

21

What is the decimal equivalent of 1001₂?

9

What is the decimal equivalent of 101010110₂?

342

What is the decimal equivalent of 101010₂?

42

What is the decimal equivalent of 110111₂?

55