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:
1010 1000 1000 0011 1001 0000 0000 0100 = 010 1000 1000 0011 1001 0000 0000 0100
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
0 229
1 228
0 227
1 226
0 225
0 224
0 223
1 222
0 221
0 220
0 219
0 218
0 217
1 216
1 215
1 214
0 213
0 212
1 211
0 210
0 29
0 28
0 27
0 26
0 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.
010 1000 1000 0011 1001 0000 0000 0100(2) =
(0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 0 × 20)(10) =
(0 + 536 870 912 + 0 + 134 217 728 + 0 + 0 + 0 + 8 388 608 + 0 + 0 + 0 + 0 + 0 + 131 072 + 65 536 + 32 768 + 0 + 0 + 4 096 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 4 + 0 + 0)(10) =
(536 870 912 + 134 217 728 + 8 388 608 + 131 072 + 65 536 + 32 768 + 4 096 + 4)(10) =
679 710 724(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1010 1000 1000 0011 1001 0000 0000 0100(2) = -679 710 724(10)
The number 1010 1000 1000 0011 1001 0000 0000 0100(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1010 1000 1000 0011 1001 0000 0000 0100(2) = -679 710 724(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.