1. 168493 XML and Web Services (II/2546)
Base 2 to Base 10
Let b be a digit in the number of base 2 Then for a number of base 2, B, that has n digits, we can write them as
B = bn-1bn-2..b2b1b0
The total value of B in a decimal number, D, is
D = (bn-1x2n-1) + (bn-2x 2n-2) + …
+ (b2x22) + (b1x21) + (b0x20)
178110: Computer Programming (II/2546)
Dept. of Computer Engineering, Khon Kaen U.

2. 178110: Computer Programming (II/2546)
Examples: Base 2  Base 10
1 = 1x20 = 1
10 = 1x21 + 0x20 = 2
101 = 1x22 + 0x21 + 1x20 = = 5
= 1x24 + 1x23 + 0x22 + 0x x20 = = 25
= 1x25 + 1x24 + 1x23 + 1x x21 + 1x20 =
= 63
178110: Computer Programming (II/2546)

3. 178110: Computer Programming (II/2546)
Base 10 to Base 2
D = (bn-1x2n-1) + (bn-2x 2n-2) + …
+ (b2x22) + (b1x21) + (b0x20)
Procedure:
Keep dividing D with 2 until the number is less than 2
The answer is the concatenation of final quotient and all remainders
178110: Computer Programming (II/2546)

4. 178110: Computer Programming (II/2546)
Examples: Base 10  Base 2
13 = 11012
178110: Computer Programming (II/2546)