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:
0000 0000 0000 0000 0000 0000 0010 0000 1100 0010 0100 1101 1101 0010 1011 0010 = 000 0000 0000 0000 0000 0000 0010 0000 1100 0010 0100 1101 1101 0010 1011 0010
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
262
0 261
0 260
0 259
0 258
0 257
0 256
0 255
0 254
0 253
0 252
0 251
0 250
0 249
0 248
0 247
0 246
0 245
0 244
0 243
0 242
0 241
0 240
0 239
0 238
0 237
1 236
0 235
0 234
0 233
0 232
0 231
1 230
1 229
0 228
0 227
0 226
0 225
1 224
0 223
0 222
1 221
0 220
0 219
1 218
1 217
0 216
1 215
1 214
1 213
0 212
1 211
0 210
0 29
1 28
0 27
1 26
0 25
1 24
1 23
0 22
0 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
000 0000 0000 0000 0000 0000 0010 0000 1100 0010 0100 1101 1101 0010 1011 0010(2) =
(0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 0 × 258 + 0 × 257 + 0 × 256 + 0 × 255 + 0 × 254 + 0 × 253 + 0 × 252 + 0 × 251 + 0 × 250 + 0 × 249 + 0 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 0 × 241 + 0 × 240 + 0 × 239 + 0 × 238 + 1 × 237 + 0 × 236 + 0 × 235 + 0 × 234 + 0 × 233 + 0 × 232 + 1 × 231 + 1 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 1 × 225 + 0 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 0 × 220 + 1 × 219 + 1 × 218 + 0 × 217 + 1 × 216 + 1 × 215 + 1 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 137 438 953 472 + 0 + 0 + 0 + 0 + 0 + 2 147 483 648 + 1 073 741 824 + 0 + 0 + 0 + 0 + 33 554 432 + 0 + 0 + 4 194 304 + 0 + 0 + 524 288 + 262 144 + 0 + 65 536 + 32 768 + 16 384 + 0 + 4 096 + 0 + 0 + 512 + 0 + 128 + 0 + 32 + 16 + 0 + 0 + 2 + 0)(10) =
(137 438 953 472 + 2 147 483 648 + 1 073 741 824 + 33 554 432 + 4 194 304 + 524 288 + 262 144 + 65 536 + 32 768 + 16 384 + 4 096 + 512 + 128 + 32 + 16 + 2)(10) =
140 698 833 586(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0000 0010 0000 1100 0010 0100 1101 1101 0010 1011 0010(2) = 140 698 833 586(10)
The number 0000 0000 0000 0000 0000 0000 0010 0000 1100 0010 0100 1101 1101 0010 1011 0010(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 0010 0000 1100 0010 0100 1101 1101 0010 1011 0010(2) = 140 698 833 586(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.