Question

1. Translate the following numbers from base 2 to base 10.                                   (28)

a. 1100

b. 10101

c. 111101

d. 1000001

Answer 1

a. 1100
0     *  2^0    =  0  *  1  =  0
0     *  2^1    =  0  *  2  =  0
1     *  2^2    =  1  *  4  =  4
1     *  2^3    =  1  *  8  =  8
Sum = 0 + 0 + 4 + 8 = 12
( 1100 )2 = ( 12 )10


b. 10101
1     *  2^0    =  1  *  1  =  1
0     *  2^1    =  0  *  2  =  0
1     *  2^2    =  1  *  4  =  4
0     *  2^3    =  0  *  8  =  0
1     *  2^4    =  1  *  16 =  16
Sum = 1 + 0 + 4 + 0 + 16 = 21
( 10101 )2 = ( 21 )10


c. 111101
1     *  2^0    =  1  *  1  =  1
0     *  2^1    =  0  *  2  =  0
1     *  2^2    =  1  *  4  =  4
1     *  2^3    =  1  *  8  =  8
1     *  2^4    =  1  *  16 =  16
1     *  2^5    =  1  *  32 =  32
Sum = 1 + 0 + 4 + 8 + 16 + 32 = 61
( 111101 )2 = ( 61 )10


d. 1000001
1     *  2^0    =  1  *  1  =  1
0     *  2^1    =  0  *  2  =  0
0     *  2^2    =  0  *  4  =  0
0     *  2^3    =  0  *  8  =  0
0     *  2^4    =  0  *  16 =  0
0     *  2^5    =  0  *  32 =  0
1     *  2^6    =  1  *  64 =  64
Sum = 1 + 0 + 0 + 0 + 0 + 0 + 64 = 65
( 1000001 )2 = ( 65 )10