Question

6. Scrieți următoarele numere din baza 10 în baza 2:
a) 23; b) 37; c) 46; d) 24;
e) 72;
f) 125.​

Answer 1

 

Descompunem numere in suma de puteri ale lui 2.

Fiecare putere a lui 2 apare o singura data.

Descompunerea este unica.

Ordonam puterile descrescator.

In locul fiecarei puteri prezente scriem 1.

In locul fiecarei puteri absente scriem 0.

Rezolvare:

$\displaystyle\bf\\a)\\23=16+4+2+1\\23=2^4+2^2+2^1+2^0\\2^4~~prezent ~~1\\2^3~~absent~~~0\\2^2~~prezent~~1\\2^1~~prezent~~1\\2^0~~prezent~~1\\\\\boxed{\bf23_{(10)}=10111_{(2)}}\\\\La celelalte~nu~voi~mai~detalia~asa.\\\\b)\\37=32+4+1\\37=2^5+2^2+2^0\\Lipsesc~puterile:~2^4;~2^3;~2^1\\\\\boxed{\bf37_{(10)}=100101_{(2)}}\\\\\\c)\\46=32+8+4+2\\46=2^5+2^3+2^2+2^1\\Lipsesc~puterile:~2^4;~2^0\\\\\boxed{\bf46_{(10)}=101110_{(2)}}$

.

$\displaystyle\bf\\d)\\24=16+8\\24=2^4+2^3\\Lipsesc~puterile:~2^2;~2^1~2^0\\\\\boxed{\bf24_{(10)}=11000_{(2)}}\\\\\\e)\\72=64+8\\72=2^6+2^3\\Lipsesc~puterile:~2^5;~2^4;2^2;~2^1;~2^0\\\\\boxed{\bf24_{(10)}=11000_{(2)}}\\\\\\f)\\125=64+32+16+8+4+1\\125=2^6+2^5+2^4+2^3+2^2+2^0\\Lipsesc~puterile:~2^1\\\\\boxed{\bf125_{(10)}=1111101_{(2)}}$