Title: Conversion of base 10 numbers to other bases.

Objective:

At the end of this lesson, you will be able to convert base 10 numbers to other bases.

What you should know:

To fully understand this lesson, you should be familiar with how to perform long division and other basic arithmetic operations.

Introduction:

Conversion of a number in base 10 to other bases is as simple as performing long division -writing down the quotient of the result and the remainder.

N:B, Quotient is the number before a decimal point, e.g. in 2.2 , 2 is the quotient while the remainder is gotten by: number - (divisor x quotient), i.e 10 ÷ 4 = 2. , 2 is the quotient and the remainder is 10 - (4 x 2) => 10 - 8 = 2.

This means, 10 ÷ 4 = 2 remainder 2.

Presentation/Steps:

Given, convert 2077₁₀ to base 8, convert 45₁₀ to base 2.

To solve the above problems, the following steps will be used.

Steps:

• Divide the number by the other base value and write down the quotient and remainder.
• Divide the quotient gotten from the previous division by the other base value and write down the quotient and the remainder.
• If the quotient to be divided is less than the other base value, write 0 as the final quotient, while the quotient will be the final remainder.
• Write down the remainders starting from bottom to top.

Soln 1: 2077₁₀ to base 8

The other base value is 8.

=> 2077 ÷ 8 = Q259 R 5

=> 259 ÷ 8 = Q32 R 3

=> 32 ÷ 8 = Q4 R 0

=> 4 ÷ 8 = Q 0 R 4

The remainders from bottom to top 4035.

Therefore, 2077₁₀ to base 8 = 4035_8.

Soln 2: 45₁₀ to base 2.

The other base value is 2.

=> 45 ÷ 2 = Q12 R 1

=> 12 ÷ 2 = Q6 R 0

=> 6 ÷ 2 = Q3 R 0

=> 3 ÷ 2 = Q1 R 1

=> 1 ÷ 2 = Q 0 R 1

The remainders from bottom to top, 11001.

Therefore, 45₁₀ to base 2 = 11001₂

Summary/ Conclusion:

=> Q means Quotient and R means Remainder.

=> Always leave your answer in the converted base value.

Exercise : Convert 115₁₀ to base 6.