Why Is Binary Math Different from Decimal Math?

  • Context: High School 
  • Thread starter Thread starter MartinJH
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Discussion Overview

The discussion revolves around the differences between binary and decimal mathematics, specifically focusing on the conversion of binary numbers to their decimal equivalents. Participants explore the representation of binary digits and the calculations involved in understanding binary values.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about the binary representation of numbers, particularly the calculation of (1 * 2^3) and its relation to the binary number 1011.
  • One participant questions the presence of ones in the binary expansion, seeking clarification on their significance.
  • Another participant points out that the binary number 1011 equals 11 in decimal, while 2^3 equals 8, leading to discussions about the calculations involved.
  • Some participants provide step-by-step breakdowns of how to interpret binary numbers and the powers of 2, indicating a lack of recent practice with exponentiation.
  • Humorous remarks about the understanding of binary and mathematics are shared, highlighting varying levels of comfort with the subject matter.

Areas of Agreement / Disagreement

Participants generally agree on the basic principles of binary math but express differing levels of understanding and comfort with the calculations involved. There is no consensus on the clarity of the explanations provided, as some participants still express confusion.

Contextual Notes

Some participants acknowledge missing assumptions or a lack of recent practice with exponentiation, which may contribute to their confusion regarding binary calculations.

Who May Find This Useful

This discussion may be useful for individuals seeking to understand the fundamentals of binary mathematics, particularly those who are revisiting the topic after a long time or those who are new to the concepts.

MartinJH
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I'm a little embarrassed by this and having a total brain fart.
I understand:
(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

But for some reason I can't get this:
(1 * 2^3) is equal to 8.

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11
 
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MartinJH said:
I'm a little embarrassed by this and having a total brain fart.
I understand:
(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

But for some reason I can't get this:
(1 * 2^3) is equal to 8.

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

Why do you have ones in these terms? "(1 * 2^1) + (1 * 2^0)"
 
berkeman said:
Why do you have ones in these terms? "(1 * 2^1) + (1 * 2^0)"

I copied directly from here;
http://computer.howstuffworks.com/bytes1.htm

Its a page I came across while searching for more information. I did know how to work it out but have forgotten.
 
MartinJH said:
I copied directly from here;
http://computer.howstuffworks.com/bytes1.htm

Yes, but that adds up to 11, not 8. 1011.

What you started with was 2^3 which is 1000 which is 8Hey lookit that. I can look down and see Berkeman slooooooowly tyyyyping away... :biggrin:
 
Last edited:
MartinJH said:
I copied directly from here;
http://computer.howstuffworks.com/bytes1.htm

Its a page I came across while searching for more information. I did know how to work it out but have forgotten.

The thing you copied shows how 0b1011 = 11. (binary 1011 = 11 decimal)

Below that do you see "8 = 1000" listed?
 
Dagnabit! Beaten by Dave again :biggrin:
 
OK, thank you guys I understood :).
 
MartinJH said:
I'm a little embarrassed by this and having a total brain fart.
I understand:
(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

But for some reason I can't get this:
(1 * 2^3) is equal to 8.
So this is what you are reall9y asking about- why 1*2^3= 8?

1*2^3= 1*(2*2*2)= 1*(2*(2*2)). 2*2= 4 so that becomes 1*(2*4). 2*4= 8 so that becomes 1*8= 8.

(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11
Yes 10112 is 1*8+ 0*4+ 1*2+ 1= 11 base 10.
 
HallsofIvy said:
So this is what you are reall9y asking about- why 1*2^3= 8?

1*2^3= 1*(2*2*2)= 1*(2*(2*2)). 2*2= 4 so that becomes 1*(2*4). 2*4= 8 so that becomes 1*8= 8.Yes 10112 is 1*8+ 0*4+ 1*2+ 1= 11 base 10.
I was having trouble working out why 2^3=8. As simple as it seems. I haven't done any sort of to the power maths in years and it skipped my mind.
But yes, you had answered my question, thank you.

But ignoring the 1 in 1 * 2^3 as it was simply telling what binary digit 2^3 was representing.
 
  • #10
There are 10 kinds of people in the world. Those who read binary and those who don't.
 
  • #11
Antiphon said:
There are 10 kinds of people in the world. Those who read binary and those who don't.
Or, there are 3 kinds of people in the world: those who understand mathematics, and those who don't. :-p
 
  • #12
Mark44 said:
Or, there are 3 kinds of people in the world: those who understand mathematics, and those who don't. :-p

I don't :rolleyes:
 

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