1. Is this a positive or a negative number?
1010 1110 1011 0101 0011 1100 1101 0101 is the binary representation of a negative integer, on 32 bits (4 Bytes).
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 1110 1011 0101 0011 1100 1101 0101 = 010 1110 1011 0101 0011 1100 1101 0101
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
1 225
1 224
0 223
1 222
0 221
1 220
1 219
0 218
1 217
0 216
1 215
0 214
0 213
1 212
1 211
1 210
1 29
0 28
0 27
1 26
1 25
0 24
1 23
0 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
010 1110 1011 0101 0011 1100 1101 0101(2) =
(0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 1 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 0 × 217 + 1 × 216 + 0 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 536 870 912 + 0 + 134 217 728 + 67 108 864 + 33 554 432 + 0 + 8 388 608 + 0 + 2 097 152 + 1 048 576 + 0 + 262 144 + 0 + 65 536 + 0 + 0 + 8 192 + 4 096 + 2 048 + 1 024 + 0 + 0 + 128 + 64 + 0 + 16 + 0 + 4 + 0 + 1)(10) =
(536 870 912 + 134 217 728 + 67 108 864 + 33 554 432 + 8 388 608 + 2 097 152 + 1 048 576 + 262 144 + 65 536 + 8 192 + 4 096 + 2 048 + 1 024 + 128 + 64 + 16 + 4 + 1)(10) =
783 629 525(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1010 1110 1011 0101 0011 1100 1101 0101(2) = -783 629 525(10)
The number 1010 1110 1011 0101 0011 1100 1101 0101(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1010 1110 1011 0101 0011 1100 1101 0101(2) = -783 629 525(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.