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:
1100 1100 1110 1100 1001 1100 1000 1100 1010 1100 1000 1100 0110 1100 0100 1001 = 100 1100 1110 1100 1001 1100 1000 1100 1010 1100 1000 1100 0110 1100 0100 1001
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
262
1 261
0 260
0 259
1 258
1 257
0 256
0 255
1 254
1 253
1 252
0 251
1 250
1 249
0 248
0 247
1 246
0 245
0 244
1 243
1 242
1 241
0 240
0 239
1 238
0 237
0 236
0 235
1 234
1 233
0 232
0 231
1 230
0 229
1 228
0 227
1 226
1 225
0 224
0 223
1 222
0 221
0 220
0 219
1 218
1 217
0 216
0 215
0 214
1 213
1 212
0 211
1 210
1 29
0 28
0 27
0 26
1 25
0 24
0 23
1 22
0 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
100 1100 1110 1100 1001 1100 1000 1100 1010 1100 1000 1100 0110 1100 0100 1001(2) =
(1 × 262 + 0 × 261 + 0 × 260 + 1 × 259 + 1 × 258 + 0 × 257 + 0 × 256 + 1 × 255 + 1 × 254 + 1 × 253 + 0 × 252 + 1 × 251 + 1 × 250 + 0 × 249 + 0 × 248 + 1 × 247 + 0 × 246 + 0 × 245 + 1 × 244 + 1 × 243 + 1 × 242 + 0 × 241 + 0 × 240 + 1 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 1 × 235 + 1 × 234 + 0 × 233 + 0 × 232 + 1 × 231 + 0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 1 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 1 × 219 + 1 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 1 × 214 + 1 × 213 + 0 × 212 + 1 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20)(10) =
(4 611 686 018 427 387 904 + 0 + 0 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 0 + 0 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 9 007 199 254 740 992 + 0 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 0 + 0 + 140 737 488 355 328 + 0 + 0 + 17 592 186 044 416 + 8 796 093 022 208 + 4 398 046 511 104 + 0 + 0 + 549 755 813 888 + 0 + 0 + 0 + 34 359 738 368 + 17 179 869 184 + 0 + 0 + 2 147 483 648 + 0 + 536 870 912 + 0 + 134 217 728 + 67 108 864 + 0 + 0 + 8 388 608 + 0 + 0 + 0 + 524 288 + 262 144 + 0 + 0 + 0 + 16 384 + 8 192 + 0 + 2 048 + 1 024 + 0 + 0 + 0 + 64 + 0 + 0 + 8 + 0 + 0 + 1)(10) =
(4 611 686 018 427 387 904 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 9 007 199 254 740 992 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 140 737 488 355 328 + 17 592 186 044 416 + 8 796 093 022 208 + 4 398 046 511 104 + 549 755 813 888 + 34 359 738 368 + 17 179 869 184 + 2 147 483 648 + 536 870 912 + 134 217 728 + 67 108 864 + 8 388 608 + 524 288 + 262 144 + 16 384 + 8 192 + 2 048 + 1 024 + 64 + 8 + 1)(10) =
5 542 977 369 390 476 361(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1100 1100 1110 1100 1001 1100 1000 1100 1010 1100 1000 1100 0110 1100 0100 1001(2) = -5 542 977 369 390 476 361(10)
The number 1100 1100 1110 1100 1001 1100 1000 1100 1010 1100 1000 1100 0110 1100 0100 1001(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1100 1100 1110 1100 1001 1100 1000 1100 1010 1100 1000 1100 0110 1100 0100 1001(2) = -5 542 977 369 390 476 361(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.