Questions and Answers
What is the base of the binary number system?
Which digits are used in the binary number system?
What is the denary equivalent of the binary number 11101110?
Which of the following correctly represents the binary number 011110001011 in denary?
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In the binary number 11101110, which column value contributes to the total?
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The value of the binary digit in the 5th column from the right in the number 11101110 is represented by which decimal number?
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How many unique digits are used in the denary number system?
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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?
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What is the primary reason computers use the binary number system?
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Which number system is NOT commonly used in data representation for computers?
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How does binary addition differ from denary addition when it comes to overflow?
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Which of the following best describes how sound is represented digitally?
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What do character sets like ASCII and Unicode facilitate?
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What effect does color depth have on images?
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Which type of compression reduces file size without losing any data?
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What is a primary purpose of data storage measurement?
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What is the denary equivalent of the binary number 01111011?
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Which method is NOT mentioned for converting denary numbers to binary?
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How is the denary number 255 represented in binary?
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What is the result of converting the binary number 10010001 to denary?
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Which of the following binary numbers is equivalent to the denary number 2047?
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If the binary number is 000111100111, what is its denary value?
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What is the first remainder obtained when converting the denary number 59 using the successive division method?
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Using the subtraction method, what is the largest power of 2 subtracted first from the number 59?
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What is the binary representation of the denary number 59 when obtained using the two methods described?
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Which step follows after dividing 29 by 2 in the successive division method?
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What is the last remainder obtained when converting 59 into binary using successive division?
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What would be the binary number if only the remainders from the second method were read in the usual order instead of reverse?
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What is the result of subtracting the largest power of 2 from 35000 repeatedly until reaching 0?
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Which step is incorrect in the division by 2 method described for converting 35000 into binary?
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What is the binary representation of the denary number 35000 after using the successive division method?
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In Method 1 for converting 35000 to binary, which power of 2 is subtracted first?
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How many steps are involved in the successive division method until reaching a quotient of 0 when converting 35000?
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Which of these is NOT a power of 2 that was subtracted in the first method for converting 35000?
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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...).
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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.
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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.