Question

Samuel is working on decimal and binary conversion for his college project. He is using the binary number 111011 and wants to explain its conversion to the decimal number 59. Which formula will Samuel use to explain the conversion?
A)1 x 25 + 24 + 1 x 23 + 0 x 22 + 1 x 21+ 1 x 20
B)0 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 1 x 21+ 1 x 20
C)1 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 1 x 21+ 1 x 20
D)20 x 1 + 21 x 1 + 22 x 0 + 23 x 1 + 24 x 1 + 25 x 1
E)1 x 25 + 1 x 25 + 22 x 0 + 23 x 1 + 24 x 1 + 25 x 1

Answer 1

1 X 25 + 1 X 24 + 1 X 23 + 0 X 22 + 1 X 21 + 1 X 20 thus your Answer is C

Answer 2

Answer:

C)$1*2^{5} + 1*2^{4} + 1*2^{3} + 0*2^{2} + 1*2^{1} + 1*2^{0}$

Explanation:

We start the conversion from the final bit, that is, the least significant.

The counter starts at zero, and we start adding, this way:

111011

$D = 1*2^{0} + 1*2^{1} + 0*2^{2} + 1*2^{3} + 1*2^{4} + 1*2^{5} = 1*2^{5} + 1*2^{4} + 1*2^{3} + 0*2^{2} + 1*2^{1} + 1*2^{0}$

So the correct answer is:

C)$1*2^{5} + 1*2^{4} + 1*2^{3} + 0*2^{2} + 1*2^{1} + 1*2^{0}$