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:
1001 0100 1110 0110 1011 1011 0101 0100 1010 1010 1000 0000 0000 0000 0011 0000 = 001 0100 1110 0110 1011 1011 0101 0100 1010 1010 1000 0000 0000 0000 0011 0000
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
262
0 261
0 260
1 259
0 258
1 257
0 256
0 255
1 254
1 253
1 252
0 251
0 250
1 249
1 248
0 247
1 246
0 245
1 244
1 243
1 242
0 241
1 240
1 239
0 238
1 237
0 236
1 235
0 234
1 233
0 232
0 231
1 230
0 229
1 228
0 227
1 226
0 225
1 224
0 223
1 222
0 221
0 220
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
0 22
0 21
0 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
001 0100 1110 0110 1011 1011 0101 0100 1010 1010 1000 0000 0000 0000 0011 0000(2) =
(0 × 262 + 0 × 261 + 1 × 260 + 0 × 259 + 1 × 258 + 0 × 257 + 0 × 256 + 1 × 255 + 1 × 254 + 1 × 253 + 0 × 252 + 0 × 251 + 1 × 250 + 1 × 249 + 0 × 248 + 1 × 247 + 0 × 246 + 1 × 245 + 1 × 244 + 1 × 243 + 0 × 242 + 1 × 241 + 1 × 240 + 0 × 239 + 1 × 238 + 0 × 237 + 1 × 236 + 0 × 235 + 1 × 234 + 0 × 233 + 0 × 232 + 1 × 231 + 0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 1 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 0 × 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 + 1 × 24 + 0 × 23 + 0 × 22 + 0 × 21 + 0 × 20)(10) =
(0 + 0 + 1 152 921 504 606 846 976 + 0 + 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 + 0 + 1 125 899 906 842 624 + 562 949 953 421 312 + 0 + 140 737 488 355 328 + 0 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 0 + 2 199 023 255 552 + 1 099 511 627 776 + 0 + 274 877 906 944 + 0 + 68 719 476 736 + 0 + 17 179 869 184 + 0 + 0 + 2 147 483 648 + 0 + 536 870 912 + 0 + 134 217 728 + 0 + 33 554 432 + 0 + 8 388 608 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 32 + 16 + 0 + 0 + 0 + 0)(10) =
(1 152 921 504 606 846 976 + 288 230 376 151 711 744 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 9 007 199 254 740 992 + 1 125 899 906 842 624 + 562 949 953 421 312 + 140 737 488 355 328 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 2 199 023 255 552 + 1 099 511 627 776 + 274 877 906 944 + 68 719 476 736 + 17 179 869 184 + 2 147 483 648 + 536 870 912 + 134 217 728 + 33 554 432 + 8 388 608 + 32 + 16)(10) =
1 506 097 097 714 171 952(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1001 0100 1110 0110 1011 1011 0101 0100 1010 1010 1000 0000 0000 0000 0011 0000(2) = -1 506 097 097 714 171 952(10)
The number 1001 0100 1110 0110 1011 1011 0101 0100 1010 1010 1000 0000 0000 0000 0011 0000(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1001 0100 1110 0110 1011 1011 0101 0100 1010 1010 1000 0000 0000 0000 0011 0000(2) = -1 506 097 097 714 171 952(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.