Unsigned: Binary -> Integer: 1011 1011 1011 1011 1011 1000 Convert Base Two (2) Number to Base Ten (10), The Unsigned Binary Converted to a Positive Integer, Written in the Decimal System
The unsigned binary (in base two) 1011 1011 1011 1011 1011 1000(2) to a positive integer (with no sign) in decimal system (in base ten) = ?
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.
1011 1011 1011 1011 1011 1000(2) =
(1 × 223 + 0 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 0 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 0 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 0 × 20)(10) =
(8 388 608 + 0 + 2 097 152 + 1 048 576 + 524 288 + 0 + 131 072 + 65 536 + 32 768 + 0 + 8 192 + 4 096 + 2 048 + 0 + 512 + 256 + 128 + 0 + 32 + 16 + 8 + 0 + 0 + 0)(10) =
(8 388 608 + 2 097 152 + 1 048 576 + 524 288 + 131 072 + 65 536 + 32 768 + 8 192 + 4 096 + 2 048 + 512 + 256 + 128 + 32 + 16 + 8)(10) =
12 303 288(10)
The number 1011 1011 1011 1011 1011 1000(2) converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):
1011 1011 1011 1011 1011 1000(2) = 12 303 288(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.
Convert unsigned binary numbers (base two) to positive integers in the decimal system (base ten)
How to convert an unsigned binary number (base two) to a positive integer in base ten:
1) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.
2) Add all the terms up to get the integer number in base ten.