1011001₂->  89₁₀

Using the algorithm:
1 x <- dk   (move leftmost digit to x)    2 i <- k-1 (set index to next digit)    3 while i > 0 do    4     x <- di +2x (compute inner product)    5     i <- i - 1 (decrement index, end while loop)    6 stop	x <- 1 x <- 0+1*2 = 2 x <- 1+2*2 = 5 x<- 1+2*5 = 11 x <- 0+2*11 = 22 x <- 0+2*22 = 44 x <- 1+2*44 = 89

Using the "place value equation":

1011001₂ = 1·2⁶ + 0·2⁵ + 1·2⁴ + 1·2³ + 0·2² + 0·2¹ + 1·2⁰ =
1·64 + 0·32 + 1·16 + 1·8 + 0·4 + 0·2 + 1·1 =
64 + 0 + 0 + 16 + 8 + 1 = 89₁₀

497₁₀->  111110001₂

Using the algorithm:
1 s <- 0 (starting from rightmost digit)    2 while x != 0 do    3     ds <- x mod 2 (get remainder of divide by 2)    4     x <- floor(x/2) (reset x to quotient)    5     s <- s + 1 (set up for next digit)    6 stop	497/2 = 248 + 1 248/2 = 124 + 0 124/2 = 62 + 0 62/2 = 31 + 0 31/2 = 15 + 1 15/2 = 7 + 1 7/2 = 3 + 1 3/2 = 1 + 1 1/2 = 0 + 1 The writing the remainders bottom to top we get: answer = 111110001

Using the "place value equation":

497 = 1·256 + 241 = 1·2⁸ + 241
241 = 1·128 + 113 = 1·2⁷ + 113
113 = 1·64 + 49 = 1·2⁶ + 49
49 = 1·32 + 17 = 1·2⁵ + 17
17 = 1·16 + 1 = 1·2⁴ + 1
(several "won't go" conditions to produce 0s)
1 = 1·1 + 0 = 1·2⁰ + 0
Write the place-value parameters top to bottom
answer = 111110001