Question

Arătați că numărul 1998 poate fi scris ca o sumă de puteri ale lui 2

Answer 1

1998:2=999 rest 0

999:2=499 rest 1

499:2=249 rest 1

249:2=124 rest 1

124:2=62 rest 0

62:2=31 rest 0

31:2=15 rest1

15:2=7 rest 1

7:2=3 rest 1

3:2=1 rest 1

1:2=0 rest 1

1998=11111001110 (in baza 2)

deci, 1998=0•2^0+1•2^1+1•2^2+1•2^3+1•2^6+1•2^7+1•2^8+1•2^9+1•2^10

1998=2 + 2^2 + 2^3 + 2^6 + 2^7 + 2^8 + 2^9 + 2^10