Binary Number System

Computers use binary digits. And some puzzles can be solved using binary numbers.

A Binary Number is made up of only 0s and 1s.

110100 Example of a Binary Number

There is no 2,3,4,5,6,7,8 or 9 in Binary!

How do we Count using Binary?

 Binary 0 We start at 0 1 Then 1 ??? But then there is no symbol for 2... what do we do?

Decimal

Well how do we count in Decimal?

 0 Start at 0 ... Count 1,2,3,4,5,6,7,8, and then... 9 This is the last digit in Decimal 10 So we start back at 0 again, but add 1 on the left

The same thing is done in binary ...

 Binary 0 Start at 0 • 1 Then 1 •• 10 Now start back at 0 again, but add 1 on the left ••• 11 1 more •••• ??? But NOW what ... ?

Decimal What happens in Decimal ... ?

99 When we run out of digits, we ...

100 ... start back at 0 again, but add 1 on the left

And that is what we do in binary ...

Binary 0 Start at 0 • 1 Then 1 •• 10 Start back at 0 again, but add 1 on the left

 Binary 0 Start at 0 • 1 Then 1 •• 10 Now start back at 0 again, but add 1 on the left ••• 11 •••• 100 start back at 0 again, and add one to the number on the left... ... but that number is already at 1 so it also goes back to 0 ... ... and 1 is added to the next position on the left ••••• 101 •••••• 110 ••••••• 111 •••••••• 1000 Start back at 0 again (for all 3 digits), add 1 on the left ••••••••• 1001 And so on!

Binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). He base-2 system is a positional notation with a radix of 2.

 Binary 8-bits word length: 27 26 25 24 23 22 21 20 = 128 = 64 = 32 = 16 = 8 = 4 = 2 = 1

Decimal vs Binary

Here are some equivalent values:

 Decimal: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Binary 4-bits word length: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

we start counting from the right

 1 2 3 = 1 + 2 4 5 = 4 + 1 6 = 4 + 2 7 = 4 + 2 + 1 8 20 21 21 + 20 22 22 + 20 22 + 21 22 + 21 + 20 23 0001 0010 0011 0100 0101 0110 0111 1000

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