PeterBushMan Posted May 25 Share Posted May 25 binary is "base-2" system. What does "base-2" mean? Is it -- all numbers are in the form 2^x? Link to comment Share on other sites More sharing options...

joigus Posted May 25 Share Posted May 25 Mentioned as "base-2" on: https://www.scienceforums.net/search/?q=base-2&quick=1&type=forums_topic As a topic: https://www.scienceforums.net/search/?q=base-2&quick=1&type=forums_topic Mentioned as "binary system" or the like gives similar results. 30 minutes ago, PeterBushMan said: Is it -- all numbers are in the form 2^x? Not exactly. Not all numbers are powers of two, are they? It means all numbers are expanded as combinations of powers of two with multipliers (digits that are only integers less than two). That covers all numbers. Link to comment Share on other sites More sharing options...

mathematic Posted May 26 Share Posted May 26 base digits 2......0,1 3......0,1,2 4......0,1,2,3 etc. Link to comment Share on other sites More sharing options...

Eise Posted May 26 Share Posted May 26 (edited) 'Binary numbers' do not exist, neither do 'decimal numbers'. Numbers exist, but we can use different notations for them. Take the number 153, in decimal notation. This means: (1 x 100) + (5 x 10) + (3 x 1). With exponents you could write it as: (1 x 10²) + (5 x 10¹) + (3 x 10⁰). So the number is expressed as sums of multiples of powers of 10. So the base number is 10. In binary, 153 is written as 10011001, which means: (1 x 2⁷) + (0 x 2⁶) + (0 x 2⁵) +(1 x 2⁴) +(1 x 2³) + (0 x 2²) + (0 x 2¹) +(1 x 2⁰) Which is in decimal: (1 x 128) + (0 x 64) + (0 x 32)+ (1 x 16) + (1 x 8 ) + (0 x 4)+ (0 x 2) + (1 x 1) = 153. Every number can be written in every base. Edited May 26 by Eise Link to comment Share on other sites More sharing options...

PeterBushMan Posted May 27 Author Share Posted May 27 17 hours ago, Eise said: 'Binary numbers' do not exist, neither do 'decimal numbers'. Numbers exist, but we can use different notations for them. Take the number 153, in decimal notation. This means: (1 x 100) + (5 x 10) + (3 x 1). With exponents you could write it as: (1 x 10²) + (5 x 10¹) + (3 x 10⁰). So the number is expressed as sums of multiples of powers of 10. So the base number is 10. In binary, 153 is written as 10011001, which means: (1 x 2⁷) + (0 x 2⁶) + (0 x 2⁵) +(1 x 2⁴) +(1 x 2³) + (0 x 2²) + (0 x 2¹) +(1 x 2⁰) Which is in decimal: (1 x 128) + (0 x 64) + (0 x 32)+ (1 x 16) + (1 x 8 ) + (0 x 4)+ (0 x 2) + (1 x 1) = 153. Every number can be written in every base. Thanks. Link to comment Share on other sites More sharing options...

## Recommended Posts

## Create an account or sign in to comment

You need to be a member in order to leave a comment

## Create an account

Sign up for a new account in our community. It's easy!

Register a new account## Sign in

Already have an account? Sign in here.

Sign In Now