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:
0011 0111 1001 1011 0111 0111 1011 0011 = 011 0111 1001 1011 0111 0111 1011 0011
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
0 229
1 228
1 227
0 226
1 225
1 224
1 223
1 222
0 221
0 220
1 219
1 218
0 217
1 216
1 215
0 214
1 213
1 212
1 211
0 210
1 29
1 28
1 27
1 26
0 25
1 24
1 23
0 22
0 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
011 0111 1001 1011 0111 0111 1011 0011(2) =
(0 × 230 + 1 × 229 + 1 × 228 + 0 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 1 × 219 + 0 × 218 + 1 × 217 + 1 × 216 + 0 × 215 + 1 × 214 + 1 × 213 + 1 × 212 + 0 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 536 870 912 + 268 435 456 + 0 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 0 + 0 + 1 048 576 + 524 288 + 0 + 131 072 + 65 536 + 0 + 16 384 + 8 192 + 4 096 + 0 + 1 024 + 512 + 256 + 128 + 0 + 32 + 16 + 0 + 0 + 2 + 1)(10) =
(536 870 912 + 268 435 456 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 1 048 576 + 524 288 + 131 072 + 65 536 + 16 384 + 8 192 + 4 096 + 1 024 + 512 + 256 + 128 + 32 + 16 + 2 + 1)(10) =
932 935 603(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0011 0111 1001 1011 0111 0111 1011 0011(2) = 932 935 603(10)
The number 0011 0111 1001 1011 0111 0111 1011 0011(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0011 0111 1001 1011 0111 0111 1011 0011(2) = 932 935 603(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.