1. Is this a positive or a negative number?
0100 0000 1001 0000 0000 0000 0001 1110 is the binary representation of a positive integer, on 32 bits (4 Bytes).
In a signed binary, the first bit (the leftmost) is reserved for the sign,
1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
2. Construct the unsigned binary number.
Exclude the first bit (the leftmost), that is reserved for the sign:
0100 0000 1001 0000 0000 0000 0001 1110 = 100 0000 1001 0000 0000 0000 0001 1110
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
1 229
0 228
0 227
0 226
0 225
0 224
0 223
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
0 24
1 23
1 22
1 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
100 0000 1001 0000 0000 0000 0001 1110(2) =
(1 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 0 × 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 + 0 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =
(1 073 741 824 + 0 + 0 + 0 + 0 + 0 + 0 + 8 388 608 + 0 + 0 + 1 048 576 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 16 + 8 + 4 + 2 + 0)(10) =
(1 073 741 824 + 8 388 608 + 1 048 576 + 16 + 8 + 4 + 2)(10) =
1 083 179 038(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0100 0000 1001 0000 0000 0000 0001 1110(2) = 1 083 179 038(10)
The number 0100 0000 1001 0000 0000 0000 0001 1110(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0100 0000 1001 0000 0000 0000 0001 1110(2) = 1 083 179 038(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.