Number Systems in Computer Science

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the base of the binary number system?

Base 2 (correct)

Base 8

Base 10

Base 16

Which digits are used in the binary number system?

0 and 1 (correct)

0-9

A-F

1-10

What is the denary equivalent of the binary number 11101110?

238 (correct)

225

240

250

Which of the following correctly represents the binary number 011110001011 in denary?

1931 Signup and view all the answers

In the binary number 11101110, which column value contributes to the total?

All of the above Signup and view all the answers

The value of the binary digit in the 5th column from the right in the number 11101110 is represented by which decimal number?

8 Signup and view all the answers

How many unique digits are used in the denary number system?

10 Signup and view all the answers

What is the heading value of the binary column with the binary digit '1' in the 6th position from the right in the number 011110001011?

64 Signup and view all the answers

What is the primary reason computers use the binary number system?

It directly represents physical states of switches. Signup and view all the answers

Which number system is NOT commonly used in data representation for computers?

Octal Signup and view all the answers

How does binary addition differ from denary addition when it comes to overflow?

Both systems experience overflow, but binary overflow is more frequent. Signup and view all the answers

Which of the following best describes how sound is represented digitally?

By sampling at regular intervals and converting to binary. Signup and view all the answers

What do character sets like ASCII and Unicode facilitate?

Representation of text in a format that computers can process. Signup and view all the answers

What effect does color depth have on images?

It affects the range of colors displayed in the image. Signup and view all the answers

Which type of compression reduces file size without losing any data?

Lossless compression Signup and view all the answers

What is a primary purpose of data storage measurement?

To determine the maximum amount of data a device can hold. Signup and view all the answers

What is the denary equivalent of the binary number 01111011?

117 Signup and view all the answers

Which method is NOT mentioned for converting denary numbers to binary?

Successive addition of binary digits Signup and view all the answers

How is the denary number 255 represented in binary?

11111111 Signup and view all the answers

What is the result of converting the binary number 10010001 to denary?

153 Signup and view all the answers

Which of the following binary numbers is equivalent to the denary number 2047?

011111111111 Signup and view all the answers

If the binary number is 000111100111, what is its denary value?

463 Signup and view all the answers

What is the first remainder obtained when converting the denary number 59 using the successive division method?

1 Signup and view all the answers

Using the subtraction method, what is the largest power of 2 subtracted first from the number 59?

32 Signup and view all the answers

What is the binary representation of the denary number 59 when obtained using the two methods described?

111011 Signup and view all the answers

Which step follows after dividing 29 by 2 in the successive division method?

14 remainder 1 Signup and view all the answers

What is the last remainder obtained when converting 59 into binary using successive division?

1 Signup and view all the answers

What would be the binary number if only the remainders from the second method were read in the usual order instead of reverse?

011101 Signup and view all the answers

What is the result of subtracting the largest power of 2 from 35000 repeatedly until reaching 0?

1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 Signup and view all the answers

Which step is incorrect in the division by 2 method described for converting 35000 into binary?

1093, remainder: 0 Signup and view all the answers

What is the binary representation of the denary number 35000 after using the successive division method?

1 0 0 0 1 1 1 0 0 0 0 0 1 0 Signup and view all the answers

In Method 1 for converting 35000 to binary, which power of 2 is subtracted first?

32768 Signup and view all the answers

How many steps are involved in the successive division method until reaching a quotient of 0 when converting 35000?

15 Signup and view all the answers

Which of these is NOT a power of 2 that was subtracted in the first method for converting 35000?

512 Signup and view all the answers

Study Notes

Number Systems

Three key number systems in computer science: binary (base 2), denary (base 10), and hexadecimal (base 16).
Binary uses only two digits, 0 and 1, to represent all values relevant to computer systems.
Denary utilizes ten digits (0-9) for representation, commonly used in everyday calculations.

Binary Representation

Computers convert all forms of data into a binary format due to their reliance on millions of switches (transistors) that can be either ON (1) or OFF (0).
An 8-bit binary system can represent values ranging from 0 to 255.

Converting Between Number Systems

Binary to Denary: Each '1' in a binary number contributes its positional value (e.g., 128 + 64 + 32...).
Denary to Binary: Two methods:
- Successive subtraction of powers of 2 to determine bits.
- Successive division by 2, recording remainders, and reading them in reverse order to form the binary representation.

Adding Binary Numbers

Binary addition follows simple rules: 0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 10 (0 carry 1), and 1 + 1 + 1 = 11 (1 carry 1).
Care must be taken for overflow when adding binary numbers that exceed the size limit of the system.

Shifts and Logical Operations

Binary shifts are used to multiply or divide integers by powers of 2 (left shift multiplies, right shift divides).
Logical bit representation helps manage negative numbers in binary form.

Data Representation of Different Media

Text Representation: Uses character sets like ASCII (7-bit) and Unicode (supports multiple languages).
Sound Representation: Involves sound sample rate (number of samples per second) and sample resolution (bits per sample).
Image Representation: Resolution (pixels) and color depth (bits per pixel) impact image quality and size.

Data Storage and Compression

Data storage is measured in bits, bytes, kilobytes, megabytes, etc.
File sizes can be calculated by considering the resolution and color depth for images or sample rate and resolution for sounds.
Data compression is essential to manage file sizes and enhance performance, categorized into:
- Lossy Compression: Reduces file size but sacrifices some data quality.
- Lossless Compression: Reduces file size without losing any quality.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the essential number systems used in computer science, including binary, denary, and hexadecimal. This quiz covers binary representation and methods for converting between these systems. Test your knowledge of binary addition and how computers utilize these number systems for data processing.