Converting Any Base to Any Other Base

Lesson Progress

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To do this:

Then convert the result from base ten to the required base using the division method.

Convert 321_four to base two

Solution

First convert 321_fourto base 10

321_four = 3 × 4² + 2 × 4¹ + 1 × 4⁰

= 3 × 16 + 2 × 4 + 1 × 1

= 48 + 8 + 1

321_four= 57_ten

Now convert 57_ten to base two

321_four= 111001_two

Convert 101110_twoto an octal number.

Solution

Note: Octal means eight

Convert 101110_two to base ten

⁵	⁴	³	²	¹	⁰
1	0	1	1	1	0

101110_two = 1 × 2⁵ + 0 × 2⁴ + 1 × 2³ + 1 × 2² + 1 × 2¹ + 0 × 2⁰

= (1 × 32) + (0 × 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1)

= 32 + 0 + 8 + 4 + 2 + 0

= 46_ten

Now convert 46_tento octal number

⇒ 101110_two= 56_eight

🎯 JSS1 Arcade 10-question challenge

Pick the correct answer as fast as you can.

Pass Mark 70%

1. Which is the correct expansion of 321₄?

2. What is the highest digit allowed in base 8?

3. 101110₂ is equal to what number in base ten?

4. 321₄ is equal to what number in base two?

5. 534₆ is equal to what number in base ten?

JSS1: MATHEMATICS - 1ST TERM