1. Is this a positive or a negative number?
1100 0010 1100 0110 0100 0000 0100 0110 is the binary representation of a negative integer, on 32 bits (4 Bytes).
In a signed binary in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. Get the binary representation of the positive (unsigned) number.
* Run this step only if the number is negative *
Flip all the bits of the signed binary in one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1100 0010 1100 0110 0100 0000 0100 0110) = 0011 1101 0011 1001 1011 1111 1011 1001
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
231
0 230
0 229
1 228
1 227
1 226
1 225
0 224
1 223
0 222
0 221
1 220
1 219
1 218
0 217
0 216
1 215
1 214
0 213
1 212
1 211
1 210
1 29
1 28
1 27
1 26
0 25
1 24
1 23
1 22
0 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0011 1101 0011 1001 1011 1111 1011 1001(2) =
(0 × 231 + 0 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 0 × 225 + 1 × 224 + 0 × 223 + 0 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 0 × 218 + 0 × 217 + 1 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 0 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 0 + 16 777 216 + 0 + 0 + 2 097 152 + 1 048 576 + 524 288 + 0 + 0 + 65 536 + 32 768 + 0 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 0 + 32 + 16 + 8 + 0 + 0 + 1)(10) =
(536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 16 777 216 + 2 097 152 + 1 048 576 + 524 288 + 65 536 + 32 768 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 32 + 16 + 8 + 1)(10) =
1 027 194 809(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1100 0010 1100 0110 0100 0000 0100 0110(2) = -1 027 194 809(10)
The signed binary number in one's complement representation 1100 0010 1100 0110 0100 0000 0100 0110(2) converted and written as an integer in decimal system (base ten):
1100 0010 1100 0110 0100 0000 0100 0110(2) = -1 027 194 809(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.