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:
1101 0100 1001 1100 0100 1110 1001 0110 = 101 0100 1001 1100 0100 1110 1001 0110
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
1 229
0 228
1 227
0 226
1 225
0 224
0 223
1 222
0 221
0 220
1 219
1 218
1 217
0 216
0 215
0 214
1 213
0 212
0 211
1 210
1 29
1 28
0 27
1 26
0 25
0 24
1 23
0 22
1 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
101 0100 1001 1100 0100 1110 1001 0110(2) =
(1 × 230 + 0 × 229 + 1 × 228 + 0 × 227 + 1 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 1 × 214 + 0 × 213 + 0 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =
(1 073 741 824 + 0 + 268 435 456 + 0 + 67 108 864 + 0 + 0 + 8 388 608 + 0 + 0 + 1 048 576 + 524 288 + 262 144 + 0 + 0 + 0 + 16 384 + 0 + 0 + 2 048 + 1 024 + 512 + 0 + 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0)(10) =
(1 073 741 824 + 268 435 456 + 67 108 864 + 8 388 608 + 1 048 576 + 524 288 + 262 144 + 16 384 + 2 048 + 1 024 + 512 + 128 + 16 + 4 + 2)(10) =
1 419 529 878(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1101 0100 1001 1100 0100 1110 1001 0110(2) = -1 419 529 878(10)
The number 1101 0100 1001 1100 0100 1110 1001 0110(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1101 0100 1001 1100 0100 1110 1001 0110(2) = -1 419 529 878(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.