Question

determinati numarul natural x pt care au loc egalitatile:a)121 in baza 3=x in baza 4:b)34 in baza 5=x in baza 2:c)110011in baza 2=x in baza 10;c)1210 in baza 4=x in baza 31

Answer 1

[tex]\it a) 121_{(3)} = 3^2+2\cdot3+1 = 9+6+1 = 16 \\\;\\ x_{(4)} = 16_{(10)} \\\;\\ 16 = 4^2 = 100_{(4)} \Longrightarrow x = 100 [/tex]

[tex]\it \ b ) \ 34_{(5)} =3\cdot5+4 = 19_{(10)} \\\;\\ 19_{(10)} =x_{(2)},\ \ \ x = ? \\\;\\ 19 = 2^4+2+1 = 10011_{(2)} \Longrightarrow x = 10011 [/tex]

$\it c)\ \ 110011_{(2)} = 2^5+2^4+2+1 = 32+16+2+1= 51_{(10)}$