If the data type is defined as a signed type there are different types of representation - mainly the signed magnitude representation and two's complement representation.
For signed magnitude representation, yes, the sign bit was stored as the the most significant bit (MSB, i.e. the leftmost bit). MSB of 0 represent a positive figure while 1 represents negative figure. Example:
7 = 00000111 -7 = 10000111 This is simple and (relatively) human readable, however integer types are usually not kept in this way for two problems:
(1) There are two representation for zero, +0 and -0. It makes it troublesome to compare figures as it creates a special case.
(2) It is not easy to do computation (as simple as adding and subtracting). Adding two positive numbers, positive number to negative number, negative number to positive number and adding two negative numbers are four different use cases. e.g. 7+6 is straight forward
1 Carry bit 7 = 00000111 6 = 00000110 (Logic for add) .. ........ 13 = 00001101 While calculating 7+(-6) means the subtraction logic to be used instead
7 = 00000111 -6 = 10000110 (Logic for subtraction) .. ........ 1 = 00000001 Range for a 8-bit number is therefore -(2^7)+1 to 2^7-1 (i.e. -127 to +127, with two zeroes +0 and -0). Signed magnitude representation is mainly used to keep float numbers.
And that leads to the two's complement representation. Positive numbers are represented in the same way as that of signed magnitude representation. Changing sign bit takes two steps: (1) Invert all bits (change all 0 to 1 and 1 to 0) (2) Add one.
Example, to get the representation of -6 we take following steps
6 = 00000110 Invert all bits: 11111001 Add one: 11111010 So -6 is represented as 11111010. With two's complement representation, you can still read the sign from the MSB; while there is only one representation for zero: 00000000.
It is easy to do computation with binary numbers in two's complement representation as well - adding is adding. Let's see again how it works to compute 7+(-6):
1111111 Carry bit 7 = 00000111 -6 = 11111010 (Logic for add) .. ........ 1 = 00000001 Range for a 8-bit number is therefore -(2^7) to 2^7-1 (i.e. -128 to +127). Note that the range is different from the signed magnitude representation.