How to convert a signed binary:
0011 1111 0111 1111 1111 1111 1111 1010(2)
to an integer in decimal system (in base 10)
1. Is this a positive or a negative number?
In a signed binary, first bit (the leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
0011 1111 0111 1111 1111 1111 1111 1010 is the binary representation of a positive integer, on 32 bits (4 Bytes).
2. Construct the unsigned binary number, exclude the first bit (the leftmost), that is reserved for the sign:
0011 1111 0111 1111 1111 1111 1111 1010 = 011 1111 0111 1111 1111 1111 1111 1010
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
1 226
1 225
1 224
1 223
0 222
1 221
1 220
1 219
1 218
1 217
1 216
1 215
1 214
1 213
1 212
1 211
1 210
1 29
1 28
1 27
1 26
1 25
1 24
1 23
1 22
0 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up:
011 1111 0111 1111 1111 1111 1111 1010(2) =
(0 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 0 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 1 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 0 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 0 + 2 + 0)(10) =
(536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 2)(10) =
1 065 353 210(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0011 1111 0111 1111 1111 1111 1111 1010(2) = 1 065 353 210(10)
Conclusion:
Number 0011 1111 0111 1111 1111 1111 1111 1010(2) converted from signed binary to an integer in decimal system (in base 10):
0011 1111 0111 1111 1111 1111 1111 1010(2) = 1 065 353 210(10)
Spaces used to group digits: for binary, by 4; for decimal, by 3.
More operations of this kind:
Convert signed binary numbers to integers in decimal system (base 10)
First bit (the leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - otherwise extra bits on 0 will be added in front (to the left).