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:
0111 1110 1010 1111 0101 0111 0101 1101 = 111 1110 1010 1111 0101 0111 0101 1101
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
1 229
1 228
1 227
1 226
1 225
1 224
0 223
1 222
0 221
1 220
0 219
1 218
1 217
1 216
1 215
0 214
1 213
0 212
1 211
0 210
1 29
1 28
1 27
0 26
1 25
0 24
1 23
1 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
111 1110 1010 1111 0101 0111 0101 1101(2) =
(1 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 1 × 221 + 0 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 0 × 215 + 1 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 0 + 8 388 608 + 0 + 2 097 152 + 0 + 524 288 + 262 144 + 131 072 + 65 536 + 0 + 16 384 + 0 + 4 096 + 0 + 1 024 + 512 + 256 + 0 + 64 + 0 + 16 + 8 + 4 + 0 + 1)(10) =
(1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 8 388 608 + 2 097 152 + 524 288 + 262 144 + 131 072 + 65 536 + 16 384 + 4 096 + 1 024 + 512 + 256 + 64 + 16 + 8 + 4 + 1)(10) =
2 125 420 381(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0111 1110 1010 1111 0101 0111 0101 1101(2) = 2 125 420 381(10)
The number 0111 1110 1010 1111 0101 0111 0101 1101(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0111 1110 1010 1111 0101 0111 0101 1101(2) = 2 125 420 381(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.