Unsigned: Binary -> Integer: 11 1111 1001 0000 0000 0000 0010 1011 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) 11 1111 1001 0000 0000 0000 0010 1011(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.
229
1 228
1 227
1 226
1 225
1 224
1 223
1 222
0 221
0 220
1 219
0 218
0 217
0 216
0 215
0 214
0 213
0 212
0 211
0 210
0 29
0 28
0 27
0 26
0 25
1 24
0 23
1 22
0 21
1 20
1
2. Multiply each bit by its corresponding power of 2 and add all the terms up.
11 1111 1001 0000 0000 0000 0010 1011(2) =
(1 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =
(536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 0 + 0 + 1 048 576 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 32 + 0 + 8 + 0 + 2 + 1)(10) =
(536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 1 048 576 + 32 + 8 + 2 + 1)(10) =
1 066 401 835(10)
The number 11 1111 1001 0000 0000 0000 0010 1011(2) converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):
11 1111 1001 0000 0000 0000 0010 1011(2) = 1 066 401 835(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.