Shumëzimi i numrave binarë

Numrat Binare

y-bartja 2y- për shkak te numrave binare Psh. 3=1+2*1 dmth. bartja është 1, 3=z, kurse 1 është pozita (x).

$a_2{a}_1{a}_0$

$b_2{b}_1{b}_0$

$x_4{x}_3{x}_2{x}_1{x}_0$

${}_0=a_0{b}_0=z_0=x_0+2y_1$

${}_1=y_1+a_1{b}_0+a_0{b}_1=z_1=x_1+2y_2$

${}_2=y_2+a_2{b}_0+a_1{b}_1+a_0{b}_2=z_2=x_2+2y_2$

${}_3=y_3+a_2{b}_1+a_1{b}_2=z_3=x_3+2y_4$

${}_4=y_4+a_2{b}_2=z_4=x_4+2y_5$

${}_5=y_5$

$a_2{a}_1{a}_0$

$b_2{b}_1{b}_0$

$c_2{c}_1{c}_0$

___________________

$x_6{x}_5{x}_4{x}_3{x}_2{x}_1{x}_0$

${}_0=a_0{b}_0{c}_0=z_0=x_0+2y_1$

${}_1=y_1+a_1{b}_0{c}_0+a_0{b}_1{c}_0+a_0{b}_0{c}_1=z_1=x_1+2y_2$

${}_2=y_2+a_2{b}_0{c}_0+a_1{b}_1{c}_0+a_1{b}_0{c}_1+a_0{b}_2{c}_0+a_0{b}_1{c}_1+a_0{b}_0{c}_2=z_2=x_2+2y_2$

${}_3=y_3+a_2{b}_1{c}_0+a_2{b}_0{c}_1+a_1{b}_2{c}_0+a_1{b}_1{c}_1+a_1{b}_0{c}_2+a_0{b}_2{c}_1+a_0{b}_1{c}_2=z_3=x_3+2y_4$

${}_4=y_4+a_2{b}_2{c}_0+a_2{b}_1{c}_1+a_2{b}_0{c}_2+a_1{b}_2{c}_1+a_1{b}_1{c}_1+a_0{b}_2{c}_2=z_4=x_4+2y_5$

${}_5=y_5+a_2{b}_2{c}_1+a_2{b}_1{c}_2+a_1{b}_2{c}_2=z_5=x_5+2y_6$

${}_6=y_6+a_2{b}_2{c}_2=z_6=x_6+2y_7$

${}_7=y_7$

Sipas formules :

$a_2{a}_1{a}_0$

$b_2{b}_1{b}_0$

$c_2{c}_1{c}_0$

_________________________

$x_6{x}_5{x}_4{x}_3{x}_2{x}_1{x}_0$

${}_0=a_0{b}_0{c}_0=z_0=x_0+2y_1$

${}_1=y_1+a_1{b}_0{c}_0+a_0{b}_1{c}_0+a_0{b}_0{c}_1=z_1=x_1+2y_2$

${}_2=y_2+a_2{b}_0{c}_0+a_1{b}_1{c}_0+a_1{b}_0{c}_1+a_0{b}_2{c}_0+a_0{b}_1{c}_1+a_0{b}_0{c}_2=z_2=x_2+2y_2$

${}_3=y_3+a_2{b}_1{c}_0+a_2{b}_0{c}_1+a_1{b}_2{c}_0+a_1{b}_1{c}_1+a_1{b}_0{c}_2+a_0{b}_2{c}_1+a_0{b}_1{c}_2=z_3=x_3+2y_4$

${}_4=y_4+a_2{b}_2{c}_0+a_2{b}_1{c}_1+a_2{b}_0{c}_2+a_1{b}_2{c}_1+a_1{b}_1{c}_1+a_0{b}_2{c}_2=z_4=x_4+2y_5$

${}_5=y_5+a_2{b}_2{c}_1+a_2{b}_1{c}_2+a_1{b}_2{c}_2=z_5=x_5+2y_6$

${}_6=y_6+a_2{b}_2{c}_2=z_6=x_6+2y_7$

${}_7=y_7$

$1_2{0}_1{1}_0$

$1_2{1}_1{0}_0$

$1_2{1}_1{1}_0$

______________________

$1_7{1}_6{0}_5{1}_4{0}_3{0}_2{1}_1{0}_0$

${}_0=1\ast 0\ast 1=0=0+2\ast 0$

${}_1=0+0\ast 0\ast 0+1\ast 1\ast 1+1\ast 0\ast 1=1=1+2\ast 0$

${}_2=0+1\ast 0\ast 1+0\ast 1\ast 1+0\ast 0\ast 1+1\ast 1\ast 1+1\ast 1\ast 1+1\ast 0\ast 1=2=0+2\ast 1$

${}_3=1+1\ast 1\ast 1+1\ast 0\ast 1+0\ast 1\ast 1+0\ast 1\ast 1+0\ast 0\ast 1+1\ast 1\ast 1+1\ast 1\ast 1=4=0+2\ast 2$

${}_4=2+1\ast 1\ast 1+1\ast 1\ast 1+1\ast 0\ast 1+0\ast 1\ast 1+0\ast 1\ast 1+1\ast 1\ast 1=5=1+2\ast 2$

${}_5=2+1\ast 1\ast 1+1\ast 1\ast 1+0\ast 1\ast 1=4=0+2\ast 2$

${}_6=2+1\ast 1\ast 1=3=1+2\ast 1$

${}_7=1$