Signed and Unsigned Integers

I am going over some revision and I came across a question that asked what is 10011001 in signed integer and unsigned. I know the unsigned integer is 153 because there are no negatives in unsigned integers, but am I correct to say the signed integer of 10011001 is -153 or am I making a mistake ?

Solution

This difference between unsigned and signed number is that one of the bit is used to indicate positive or negative number.

So in your example you have 8 bits.

If I treat is as signed, then I have 7 bits to work with: 2^7

000 0000 = 0
111 1111 = 127
001 1001 = 25 then the most significant bit cause the following calculation to occurred.
(25 - 128) = -103

If I use all 8 bits then I unsigned bits to work with: 2^8

0000 0000 = 0
1111 1111 = 255
1001 1001 = 153

Here is code to demonstrate the answer:

char *endptr;
char binary[11] = "10011001";  // need an extra char for the termination

char x = (char)strtol(binary, &endptr, 2);
unsigned char y = (unsigned char)strtol(binary, &endptr, 2);

printf("%s to   signed char (1 byte): %i\n", binary, (short)x);
printf("%s to unsigned char (1 byte): %u\n", binary, y);

Output:

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