Scrieti-mmi in baza 10 si in baza 2 fiecare numar: 23, 31, 43, 59, 85, 103 si 207, si sa ma ajutati putin si la explicatii
Răspunsuri la întrebare
Iti dau cateva exemple si apoi te descurci singur.
23₁₀ = 2·10¹ + 3·10⁰
43₁₀ = 4·10¹ + 3·10⁰
103₁₀ = 110² + 310⁰
207₁₀ = 210² + 710°
Acum in baza 2 ...
23 : 2 = 11 + 1
11 : 2 = 5 + 1
5 : 2 = 2 + 1
2 : 2 = 1 + 0
1 : 2 = 0 + 1
Numarul va fi 10111
85 : 2 = 42 + 1
42 : 2 = 21 + 0
21 : 2 = 10 + 1
10 : 2 = 5 + 0
5 : 2 = 2 + 1
2 : 2 = 1 + 0
1 : 2 = 0 + 1
Numarul va fi 1010101
103 : 2 = 51 + 1
51 : 2 = 25 + 1
25 : 2 = 12 + 1
12 : 2 = 6 + 0
6 : 2 = 3 + 0
3 : 2 = 1 + 1
1 : 2 = 0 + 1
Numarul va fi 1100111
23:2=11+1
11:2=5+1
5:2=2+1
2:2=1+0
1:2=0+1 => 23₍₁₀₎=10111₍₂₎
31:2=15+1
15:2=7+1
7:2=3+1
3:2=1+1
1:2=0+1 => 31₍₁₀₎=11111₍₂₎
43:2=21+1
21:2=10+1
10:2=5+0
5:2=2+1
2:2=1+0
1:2=0+1 => 43₍₁₀₎=101011₍₂₎
59:2=29+1
29:2=14+1
14:2=7+0
7:2=3+1
3:2=1+1
1:2=0+1 => 59₍₁₀₎=111011₍₂₎
85:2=42+1
42:2=21+0
21:2=10+1
10:2=5+0
5:2=2+1
2:2=1+0
1:2=0+1 =>85₍₁₀₎=1010101₍₂₎
103:2=51+1
51:2=25+1
25:2=12+1
12:2=6+0
6:2=3+0
3:2=1+1
1:2=0+1 ....=> 103₍₁₀₎=1100111₍₂₎
207:2=103+1
103:2=51+1
51:2=25+1
25:2=12+1
12:2=6+0
6:2=3+0
3:2=1+1
1:2=0+1 => 207₍₁₀₎=11001111₍₂₎
23₍₁₀₍=10111₍₂₎ => 10111₍₂₎=(1*2⁴+0*2³+1*2²+1*2¹+1*2⁰)₍₁₀₎=
=(16+0+4+2+1)₍₁₀₎=
=23₍₁₀₎
31₍₁₀₎=11111₍₂₎ => 11111₍₂₎=(1*2⁴+1*2³+1*2²+1*2¹+1*2⁰)₍₁₀₎=
=(16+8+4+2+1)₍₁₀₎=
=31₍₁₀₎
43₍₁₀₎=101011₍₂₎ => 101011₍₂₎=(1*2⁵+0*2⁴+1*2³+0*2²+1*2¹+1*2⁰)₍₁₀₎=
=(32+0+8+0+2+1)₍₁₀₎=
=43₍₁₀₎
59₍₁₀₎=111011₍₂₎ => 111011₍₂₎=(1*2⁵+1*2⁴+1*2³+0*2²+1*2¹+1*2⁰)₍₁₀₎=
=(32+16+8+0+2+1)₍₁₀₎=
=59₍₁₀₎
85₍₁₀₎=1010101₍₂₎ =>1010101₍₂₎=(1*2⁶+0*2⁵+1*2⁴+0*2³+1*2²+0*2¹+1*2⁰)₍₁₀₎=
=(64+0+16+0+4+0+1)₍₁₀₎=
=85₍₁₀₎
103₍₁₀₎=1100111₍₂₎ => 1100111₍₂₎=(1*2⁶+1*2⁵+0*2⁴+0*2³+1*2²+1*2¹+1*2⁰)₍₁₀₎=
=(64+32+0+0+4+2+1)₍₁₀₎=
=103₍₁₀₎
207₍₁₀₎=11001111₍₂₎ => 11001111₍₂₎=(1*2⁷+1*2⁶+0*2⁵+0*2⁴+1*2³+1*2²+1*2¹+1*2⁰)₍₁₀₎=
=(128+64+0+0+8+4+2+1)₍₁₀₎=
=207₍₁₀₎