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:
1000 0000 0000 0000 1010 1101 1100 1101 = 000 0000 0000 0000 1010 1101 1100 1101
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
0 229
0 228
0 227
0 226
0 225
0 224
0 223
0 222
0 221
0 220
0 219
0 218
0 217
0 216
0 215
1 214
0 213
1 212
0 211
1 210
1 29
0 28
1 27
1 26
1 25
0 24
0 23
1 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
000 0000 0000 0000 1010 1101 1100 1101(2) =
(0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 1 × 211 + 1 × 210 + 0 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 32 768 + 0 + 8 192 + 0 + 2 048 + 1 024 + 0 + 256 + 128 + 64 + 0 + 0 + 8 + 4 + 0 + 1)(10) =
(32 768 + 8 192 + 2 048 + 1 024 + 256 + 128 + 64 + 8 + 4 + 1)(10) =
44 493(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1000 0000 0000 0000 1010 1101 1100 1101(2) = -44 493(10)
The number 1000 0000 0000 0000 1010 1101 1100 1101(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1000 0000 0000 0000 1010 1101 1100 1101(2) = -44 493(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.