Computing Systems and Number Systems

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Questions and Answers

What is the first step in converting a decimal number to another base?

Multiply the decimal number by the new base

Divide the decimal number by the new base (correct)

Replace the original decimal number with the quotient

Ignore the remainder

What is the binary equivalent of the decimal number 13?

1110

1000

1101 (correct)

1011

During the conversion of 93 from decimal to octal, what is the second remainder obtained?

3 (correct)

What is the process called when converting a decimal number into a different base?

Base conversion algorithm Signup and view all the answers

What base is used when converting the decimal number 93 to hexadecimal?

Base 16 Signup and view all the answers

What is the Base 10 equivalent of the number 642 in Base 8?

418 Signup and view all the answers

In positional notation, the value of the digit in the hundreds place of 642 in Base 10 is represented as which of the following?

6 x 10² Signup and view all the answers

What is the remainder when 93 is divided by 16?

13 Signup and view all the answers

When converting the hexadecimal number DEF to decimal, what is the value of E in positional notation?

14 x 16¹ Signup and view all the answers

What is the equivalent hexadecimal representation for the binary number 10101011?

AB Signup and view all the answers

How many groups of three are formed when converting the binary number 10101011 to octal?

2 Signup and view all the answers

Which of the following represents the value of the digit 4 in the base 13 numeral system when expressed in Base 10?

4 x 13¹ Signup and view all the answers

Which digits are used in a base 16 (Hexadecimal) system?

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Signup and view all the answers

What is the decimal equivalent of the binary number 1101110?

110 Signup and view all the answers

What is the Base 10 equivalent of the base 2 binary number 1011?

11 Signup and view all the answers

What digit in base 16 replaces 13?

D Signup and view all the answers

In the conversion from 642 in base 13 to Base 10, what is the final result?

1068 Signup and view all the answers

Which of the following is a step in converting binary to octal?

Convert each group of three Signup and view all the answers

In a typical base calculator, which base is directly used for calculations?

Base 10 Signup and view all the answers

In the decimal system, how many digit symbols are there?

10 Signup and view all the answers

What does the concept of abstraction in computing allow users to do?

Hide complex details and focus only on necessary information. Signup and view all the answers

In the binary system, what is the value of the leftmost digit in the number 1101110?

64 Signup and view all the answers

Which of the following is NOT considered hardware?

Operating system Signup and view all the answers

Which of the following best describes a rational number?

A number that can be made by dividing two integers. Signup and view all the answers

In the context of number systems, which operation involves changing a number from base 10 to base 2?

Conversion Signup and view all the answers

When dealing with multimedia, which of the following categories is NOT typically handled by modern computers?

Handwriting Signup and view all the answers

What is the primary focus of the initial chapters of this course?

Understanding how computing systems operate. Signup and view all the answers

How do binary values differ from decimal values?

Binary values are computer-oriented while decimal values are human-oriented. Signup and view all the answers

Which of the following best describes the relationship between bases 2, 8, and 16?

Base 8 and base 16 can be represented using binary values. Signup and view all the answers

What is the binary representation of the decimal number 893?

1101111101 Signup and view all the answers

When converting the decimal number 956 to hexadecimal, what is the resulting value?

3BC Signup and view all the answers

What is the result of adding the binary numbers 1101011 and 1111011?

11100110 Signup and view all the answers

What is the binary result of subtracting the binary number 0111 from 1100?

0101 Signup and view all the answers

In binary addition, what is the outcome of 1 + 1?

0 with a carry of 1 Signup and view all the answers

How many distinct values can a single binary digit (bit) represent?

2 Signup and view all the answers

What is the result of subtracting the binary number 01001 from 11010?

10001 Signup and view all the answers

What is the hexadecimal equivalent of the binary number 10110011?

B3 Signup and view all the answers

Which of the following represents the octal addition of 157 and 645?

1024 Signup and view all the answers

In binary, what is the result of 1 + 1 + 1?

10 with a carry of 1 Signup and view all the answers

Study Notes

Computing Systems Layers

Computing systems are organized in layers
Abstraction: we can interact with computers without understanding the complexity of each layer
Hardware: Physical parts like circuit boards, wires, keyboards
Software: Programs that provide instructions for the computer to execute

Data and Computers

Early computers dealt primarily with numeric and textual data
Computers today handle a variety of information types:
- Numbers
- Text
- Audio
- Video
- Images and graphics

Number Systems

Decimal system (base 10) is human-oriented
Binary system (base 2) is computer-oriented
Positional notation: the value of each digit depends on its position

Base Conversion

To convert numbers in different bases to decimal: multiply each digit by the corresponding power of the base and add the results.
To convert decimal numbers to other bases: repeatedly divide by the new base, keeping track of the remainders, which are the digits in the new base.
Base 16 (hexadecimal): uses digits 0-9 and letters A-F
Base 8 (octal): uses digits 0-7
Binary to octal: group binary digits into three and convert each group to its octal equivalent
Binary to hexadecimal: group binary digits into four and convert each group to its hexadecimal equivalent

Arithmetic Operations in Binary

Binary addition:
- 0 + 0 = 0
- 1 + 0 = 1
- 1 + 1 = 10 (carry 1)
Binary subtraction:
- 1 – 0 = 1
- 10 – 1 = 1 (borrow 1)
- 11 – 1 = 10 (carry 1)

Bits and Bytes

Bits: Binary digits, represent 0 (low voltage) or 1 (high voltage)
Byte: Group of eight bits

Converting Between Binary, Octal and Hexadecimal

Binary to octal: group by threes
Binary to hexadecimal: group by fours
Octal to binary: convert each octal digit to its three-bit binary equivalent
Hexadecimal to binary: convert each hexadecimal digit to its four-bit binary equivalent

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Description

Explore the layers of computing systems, including hardware and software, and understand how early computers managed data. This quiz also covers number systems, including decimal and binary systems, and how to convert between them.