Binary and Decimal Number Systems
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Questions and Answers

What is the base of the binary number system?

  • Base 8
  • Base 10
  • Base 2 (correct)
  • Base 16

Which digit in a binary number represents the on state?

  • 2
  • 1 (correct)
  • 0
  • Both 0 and 1

What algorithm can be used to convert a decimal number to binary?

  • Subtraction Algorithm
  • Multiplication Algorithm
  • Division Algorithm (correct)
  • Addition Algorithm

In the binary number 11101101, which digit is the least significant?

<p>1 (last digit) (C)</p> Signup and view all the answers

What remainder sequence is obtained when converting the decimal number 67 to binary using the Division Algorithm?

<p>110010 (D)</p> Signup and view all the answers

What is the base of the decimal number system?

<p>Base 10 (D)</p> Signup and view all the answers

In the decimal system, what is the value of the digit 7 in the number 572?

<p>70 (C)</p> Signup and view all the answers

If a number is expressed in base 10, how would the number 15 be represented in base 2?

<p>1111 (D)</p> Signup and view all the answers

Which statement about the decimal system is true?

<p>It includes a concept of place value. (D)</p> Signup and view all the answers

What is the decimal equivalent of the binary number (10101101)2?

<p>173 (C)</p> Signup and view all the answers

In the multiplication algorithm for binary to decimal conversion, how are the binary digits treated?

<p>They are multiplied by increasing powers of two. (B)</p> Signup and view all the answers

Which of the following steps is NOT part of the binary to decimal conversion via the multiplication algorithm?

<p>Convert binary digits to their ASCII values. (B)</p> Signup and view all the answers

What do you do after multiplying the binary digits by their positional values in the multiplication algorithm?

<p>Sum the products of the multiplications. (B)</p> Signup and view all the answers

If a binary number has the digits 1 in positions 7, 5, and 1, what would be the decimal contribution of these positions?

<p>128 + 32 + 2 (C)</p> Signup and view all the answers

Flashcards

Decimal System

A numbering system with ten unique digits (0-9) where each digit's position represents a power of ten.

Numbering System

A system for representing numbers using a fixed set of symbols, each representing a specific value.

Base of a Numbering System

The base of a numbering system determines the number of unique symbols used to represent values.

Positional Value

The positional value of a digit in a number determines its contribution based on the base of the system.

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Number Base Conversion

Converting numbers between bases involves changing the representation while maintaining the same numerical value.

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Binary Number System (Base 2)

A numbering system with two digits, 0 and 1, representing off and on states of electrical signals in computers.

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Division Algorithm

A method to convert a decimal number to its binary equivalent. It repeatedly divides the decimal number by 2, recording the quotient and remainder. The remainders form the binary digits in reverse order.

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Most Significant Digit (MSD)

The most significant digit in a binary number, representing the highest power of 2.

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Least Significant Digit (LSD)

The least significant digit in a binary number, representing the lowest power of 2.

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Decimal to Binary Conversion

The process of converting a decimal number to its equivalent in another numbering system, like binary.

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Multiplication Algorithm for Binary-Decimal Conversion

The easiest method for converting a binary number to its decimal equivalent. It involves multiplying each binary digit by increasing powers of two, starting from the rightmost digit, and then summing these products.

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Positional Value in Binary

Represents the value assigned to a digit based on its position within a number. For example, in the binary number (1010)2, the first digit (1) has a positional value of 23 (8), the second digit (0) has a positional value of 22 (4), and so on.

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Base-2 Number System (Binary)

The base of a binary number is 2, meaning it uses only two digits (0 and 1). Each digit represents a power of two, starting from 20 (1) for the rightmost digit.

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Decimal Equivalent Calculation from Binary

To convert a binary number to decimal, you sum the weights of the positions where the binary digits have a value of 1. For example, in (1101)2, the first digit (1) contributes 23 (8), the second digit (1) contributes 22 (4), and the third digit (0) contributes 21 (2).

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Base Conversion

The process of transforming a representation of a number from one base (e.g., binary) to another base (e.g., decimal). It involves maintaining the same numerical value.

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