 Quandaries and Queries

Name: david

Level: Middle

Question:
could you please explain to me how 1+1=10 thanks

Hi David,

One plus one is two, so what is going on if you write two as 10? (One warning here. Read 10 as one-zero not ten. It's not ten, it's two but written one-zero.) One place that the number two is written 10 is in base 2 arithmetic. I want to say something about base 10 arithmetic first.

In base 10 arithmetic we have ten symbols for digits. They are 0,1,2,3,4,5,6,7,8, and 9. We write the counting numbers using these symbols.

NumberBase ten representation
zero0
one1
two2
three3
.
.
.
.
.
.
nine9

At this point we run out of digits and the solution is to place the smallest non-zero digit in the second column and start again with 0 in the first column

NumberBase ten representation
zero0
one1
two2
three3
.
.
.
.
.
.
nine9
ten10
eleven11
twelve12
.
.
.
.
.
.

If you are working in base two you only have two symbols for digits, 0 and 1. Thus if you start to write the counting numbers you run out of symbols much earlier

NumberBase two representation
zero0
one1

The solution is the same as it was for the base ten representation, place the smallest non-zero digit in the second column and start again with 0 in the first column

NumberBase two representation
zero0
one1
two10
three11

Again you have run out of digits, (In base 10 this happens at ninty-nine.) so place a 1 in the next column and continue

NumberBase two representation
zero0
one1
two10
three11
four100
five101
six110
.
.
.
.
.
.

I hope this helps,
Penny

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