1. Is this a positive or a negative number?
1010 0001 is the binary representation of a negative integer, on 8 bits.
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 0001 = 010 0001
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
26
0 25
1 24
0 23
0 22
0 21
0 20
1
The number 1010 0001(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1010 0001(2) = -33(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.