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:
1011 1110 0100 0001 0010 0010 0111 1111 = 011 1110 0100 0001 0010 0010 0111 1111
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
0 229
1 228
1 227
1 226
1 225
1 224
0 223
0 222
1 221
0 220
0 219
0 218
0 217
0 216
1 215
0 214
0 213
1 212
0 211
0 210
0 29
1 28
0 27
0 26
1 25
1 24
1 23
1 22
1 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
011 1110 0100 0001 0010 0010 0111 1111(2) =
(0 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 0 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 1 × 216 + 0 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 0 + 0 + 4 194 304 + 0 + 0 + 0 + 0 + 0 + 65 536 + 0 + 0 + 8 192 + 0 + 0 + 0 + 512 + 0 + 0 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
(536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 4 194 304 + 65 536 + 8 192 + 512 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
1 044 456 063(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1011 1110 0100 0001 0010 0010 0111 1111(2) = -1 044 456 063(10)
The number 1011 1110 0100 0001 0010 0010 0111 1111(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1011 1110 0100 0001 0010 0010 0111 1111(2) = -1 044 456 063(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.