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In a certain number system, the number 1234 represents the decimal number 1*8^3

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Question: In a certain number system, the number 1234 represents the decimal number 1*8^3 + 2*8^2 + 3*8^1 + 4*8^0. What is the base of this number system?

Options:

  1. 2
  2. 8
  3. 10
  4. 16

Correct Answer: 8

Solution: 

The number 1234 is expressed in base 8, as indicated by the powers of 8 used in its representation.

In a certain number system, the number 1234 represents the decimal number 1*8^3

Practice Questions

Q1
In a certain number system, the number 1234 represents the decimal number 1*8^3 + 2*8^2 + 3*8^1 + 4*8^0. What is the base of this number system?
  1. 2
  2. 8
  3. 10
  4. 16

Questions & Step-by-Step Solutions

In a certain number system, the number 1234 represents the decimal number 1*8^3 + 2*8^2 + 3*8^1 + 4*8^0. What is the base of this number system?
  • Step 1: Identify the number given in the question, which is 1234.
  • Step 2: Understand that the number is expressed in a certain base system.
  • Step 3: Recognize that the digits in the number (1, 2, 3, 4) are multiplied by powers of the base.
  • Step 4: Notice that the highest digit (1) is in the 8^3 place, which means the base is likely 8.
  • Step 5: Confirm that the other digits (2, 3, 4) follow the same pattern with decreasing powers of 8 (8^2, 8^1, 8^0).
  • Step 6: Conclude that since the powers of 8 are used, the base of this number system is 8.
  • Base Number Systems – Understanding how numbers are represented in different bases, specifically how to convert from a base to decimal using powers of the base.
  • Positional Notation – The concept that the position of a digit in a number determines its value based on the base.
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