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 0011 0101 0101 0100 1000 1000 0101 = 100 0011 0101 0101 0100 1000 1000 0101
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
1 224
1 223
0 222
1 221
0 220
1 219
0 218
1 217
0 216
1 215
0 214
1 213
0 212
0 211
1 210
0 29
0 28
0 27
1 26
0 25
0 24
0 23
0 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
100 0011 0101 0101 0100 1000 1000 0101(2) =
(1 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 1 × 225 + 1 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 0 × 217 + 1 × 216 + 0 × 215 + 1 × 214 + 0 × 213 + 0 × 212 + 1 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(1 073 741 824 + 0 + 0 + 0 + 0 + 33 554 432 + 16 777 216 + 0 + 4 194 304 + 0 + 1 048 576 + 0 + 262 144 + 0 + 65 536 + 0 + 16 384 + 0 + 0 + 2 048 + 0 + 0 + 0 + 128 + 0 + 0 + 0 + 0 + 4 + 0 + 1)(10) =
(1 073 741 824 + 33 554 432 + 16 777 216 + 4 194 304 + 1 048 576 + 262 144 + 65 536 + 16 384 + 2 048 + 128 + 4 + 1)(10) =
1 129 662 597(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0100 0011 0101 0101 0100 1000 1000 0101(2) = 1 129 662 597(10)
The number 0100 0011 0101 0101 0100 1000 1000 0101(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0100 0011 0101 0101 0100 1000 1000 0101(2) = 1 129 662 597(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.