Converting Bases

Front

What is base conversion?

Back

Base conversion is the process of changing a number from one base (or numeral system) to another, such as from base 10 (decimal) to base 2 (binary) or vice versa.

Front

How do you convert a number from base 9 to base 10?

Back

To convert from base 9 to base 10, multiply each digit of the base 9 number by 9 raised to the power of its position (starting from 0 on the right) and sum the results.

Front

Convert 8361₉ to base 10.

Back

6138

Front

What is the formula for converting a number from base b to base 10?

Back

The formula is: N = d_n * b^n + d_(n-1) * b^(n-1) + ... + d_1 * b^1 + d_0 * b^0, where d are the digits of the number.

Front

How do you convert a number from base 4 to base 10?

Back

Similar to base 9, multiply each digit of the base 4 number by 4 raised to the power of its position and sum the results.

Front

Convert 123₄ to base 10.

Back

27

Front

What is the process for converting a decimal number to another base?

Back

Divide the decimal number by the new base and record the remainder. Repeat with the quotient until it is 0. The new base number is the remainders read in reverse order.

Front

Convert 145 to base 4.

Back

2101₄

Front

What is the significance of the base in numeral systems?

Back

The base determines how many unique digits (including zero) are used to represent numbers. For example, base 10 uses digits 0-9, while base 2 uses 0 and 1.

Front

How do you convert a number from base 9 to base 10 using an example?

Back

For 867015₉: 8*9^5 + 6*9^4 + 7*9^3 + 0*9^2 + 1*9^1 + 5*9^0 = 516875.