Converting Between Different Number Systems

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2025-11-04 23:40

In this video I show how to convert between different base number systems by first writing the number in its equivalent base exponential addition form, and then changing the base. For example, converting the Base Two number 111, we first write it as 111 = 100 + 10 + 1 = 10^2 + 10^1 + 10^0. Keep in mind that the number "10" is just a transition number, so for our Base Ten we replace the equivalent value of "10" from Base Two to Base Ten — i.e. "10" = 2 in our case. Thus 111 = 2^2 + 2^1 + 2^0 = 4 + 2 + 1 = 7 in Base Ten.

Converting from bigger base numbers to smaller bases is similar but we must account for the smaller digits, and rewrite the number using the smaller base as the exponentials. For example, the Base Ten number 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0 = 1000 + 10 + 1 = 1011 in Base Two.

I also show how to convert Base Ten to any other number system through an iterative process that allows for the conversion to be automated, as in my Base Ten to Base X Excel calculator: https://1drv.ms/x/s!As32ynv0LoaIiJgVMhymuQtS2K4xgg

#math #binary #education #numbertheory #calculator

Timestamps:

Converting number systems depends on the relative value of the transition number "10" – 0:00
Most calculators use Base Ten by default – 0:59
Converting 111 from Base Two to Base Ten: write in exponential addition form and replace transition number with value in your desired number system: 2:03
Converting 111 from Base Four to Base Ten: 3:15
Converting from Base Ten to smaller base number systems requires accounting for extra digits: 4:44
Converting 10 from Base Ten to Base Two: 6:33
Converting 10 from Base Four to Base Two: 7:47
Base Ten to Base X conversion calculations using Base Eight (Octal) as an example: 8:58
Microsoft Excel Base Number conversion calculator – 12:36
11 in Base Ten = 13 in Base Eight – 14:22

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