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:
0100 0001 1010 0011 1110 1010 0001 1010 = 100 0001 1010 0011 1110 1010 0001 1010
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
1 229
0 228
0 227
0 226
0 225
0 224
1 223
1 222
0 221
1 220
0 219
0 218
0 217
1 216
1 215
1 214
1 213
1 212
0 211
1 210
0 29
1 28
0 27
0 26
0 25
0 24
1 23
1 22
0 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
100 0001 1010 0011 1110 1010 0001 1010(2) =
(1 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 1 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 1 × 214 + 1 × 213 + 0 × 212 + 1 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =
(1 073 741 824 + 0 + 0 + 0 + 0 + 0 + 16 777 216 + 8 388 608 + 0 + 2 097 152 + 0 + 0 + 0 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 0 + 2 048 + 0 + 512 + 0 + 0 + 0 + 0 + 16 + 8 + 0 + 2 + 0)(10) =
(1 073 741 824 + 16 777 216 + 8 388 608 + 2 097 152 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 2 048 + 512 + 16 + 8 + 2)(10) =
1 101 261 338(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0100 0001 1010 0011 1110 1010 0001 1010(2) = 1 101 261 338(10)
The number 0100 0001 1010 0011 1110 1010 0001 1010(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0100 0001 1010 0011 1110 1010 0001 1010(2) = 1 101 261 338(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.