Convert base two (2) number 1011 1011 1011 1011 1011 1000 to base ten (10): the unsigned binary number converted to a positive integer written in the decimal system
Unsigned binary (base 2) 1011 1011 1011 1011 1011 1000(2) to a positive integer (no sign) in decimal system (in base 10) = ?
1. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
223
1
222
0
221
1
220
1
219
1
218
0
217
1
216
1
215
1
214
0
213
1
212
1
211
1
210
0
29
1
28
1
27
1
26
0
25
1
24
1
23
1
22
0
21
0
20
0
2. Multiply each bit by its corresponding power of 2 and add all the terms up:
Number 1011 1011 1011 1011 1011 1000(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10): 1011 1011 1011 1011 1011 1000(2) = 12 303 288(10)
Spaces used to group digits: for binary, by 4; for decimal, by 3.
How to convert unsigned binary numbers from binary system to decimal? Simply convert from base two to base ten.
To understand how to convert a number from base two to base ten, the easiest way is to do it through an example - convert the number from base two, 101 0011(2), to base ten:
Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresponding power of 2 by exactly one unit each time we move to the left:
powers of 2:
6
5
4
3
2
1
0
digits:
1
0
1
0
0
1
1
Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up: