Copyright © University of Cambridge. All rights reserved.

'Binary Squares' printed from http://nrich.maths.org/

Show menu


Is there a general pattern of $1$'s and $0$'s in a binary number which is the square of a binary number containing only $1$'s? Try squares of $11$, $111$, $1111$ etc? To generalize you might use the fact that the sum of powers of two is a geometric series.