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 0101 0101 0100 0101 1011 1001 0110 0101 0101 0110 1010 1010 1000 1100 0100 = 000 0101 0101 0100 0101 1011 1001 0110 0101 0101 0110 1010 1010 1000 1100 0100
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
1 257
0 256
1 255
0 254
1 253
0 252
1 251
0 250
1 249
0 248
0 247
0 246
1 245
0 244
1 243
1 242
0 241
1 240
1 239
1 238
0 237
0 236
1 235
0 234
1 233
1 232
0 231
0 230
1 229
0 228
1 227
0 226
1 225
0 224
1 223
0 222
1 221
1 220
0 219
1 218
0 217
1 216
0 215
1 214
0 213
1 212
0 211
1 210
0 29
0 28
0 27
1 26
1 25
0 24
0 23
0 22
1 21
0 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
000 0101 0101 0100 0101 1011 1001 0110 0101 0101 0110 1010 1010 1000 1100 0100(2) =
(0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 1 × 258 + 0 × 257 + 1 × 256 + 0 × 255 + 1 × 254 + 0 × 253 + 1 × 252 + 0 × 251 + 1 × 250 + 0 × 249 + 0 × 248 + 0 × 247 + 1 × 246 + 0 × 245 + 1 × 244 + 1 × 243 + 0 × 242 + 1 × 241 + 1 × 240 + 1 × 239 + 0 × 238 + 0 × 237 + 1 × 236 + 0 × 235 + 1 × 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 + 1 × 221 + 0 × 220 + 1 × 219 + 0 × 218 + 1 × 217 + 0 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 1 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 0 × 20)(10) =
(0 + 0 + 0 + 0 + 288 230 376 151 711 744 + 0 + 72 057 594 037 927 936 + 0 + 18 014 398 509 481 984 + 0 + 4 503 599 627 370 496 + 0 + 1 125 899 906 842 624 + 0 + 0 + 0 + 70 368 744 177 664 + 0 + 17 592 186 044 416 + 8 796 093 022 208 + 0 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 0 + 0 + 68 719 476 736 + 0 + 17 179 869 184 + 8 589 934 592 + 0 + 0 + 1 073 741 824 + 0 + 268 435 456 + 0 + 67 108 864 + 0 + 16 777 216 + 0 + 4 194 304 + 2 097 152 + 0 + 524 288 + 0 + 131 072 + 0 + 32 768 + 0 + 8 192 + 0 + 2 048 + 0 + 0 + 0 + 128 + 64 + 0 + 0 + 0 + 4 + 0 + 0)(10) =
(288 230 376 151 711 744 + 72 057 594 037 927 936 + 18 014 398 509 481 984 + 4 503 599 627 370 496 + 1 125 899 906 842 624 + 70 368 744 177 664 + 17 592 186 044 416 + 8 796 093 022 208 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 68 719 476 736 + 17 179 869 184 + 8 589 934 592 + 1 073 741 824 + 268 435 456 + 67 108 864 + 16 777 216 + 4 194 304 + 2 097 152 + 524 288 + 131 072 + 32 768 + 8 192 + 2 048 + 128 + 64 + 4)(10) =
384 032 569 469 610 180(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0101 0101 0100 0101 1011 1001 0110 0101 0101 0110 1010 1010 1000 1100 0100(2) = 384 032 569 469 610 180(10)
The number 0000 0101 0101 0100 0101 1011 1001 0110 0101 0101 0110 1010 1010 1000 1100 0100(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0000 0101 0101 0100 0101 1011 1001 0110 0101 0101 0110 1010 1010 1000 1100 0100(2) = 384 032 569 469 610 180(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.