Find the decimal equivalent of the following binary numbers expressed in the 2’s complement format:
(a) 00001110;
(b) 10001110.

Solution:-
(a) The MSB bit is ‘0’, which indicates a plus sign.
The magnitude bits are 0001110.
The decimal equivalent = 0×20 +1×21+1×22 +1×23+0×24 +0×25+0×26
= 0+2+4+8+0+0+0 = 14

Therefore, 00001110 represents +14

(b) The MSB bit is ‘1’, which indicates a minus sign
The magnitude bits are therefore given by the 2’s complement of 0001110, i.e. 1110010

The decimal equivalent = 0×20 +1×21+0×22 +0×23+1×24 +1×25
+1×26
= 0+2+0+0+16+32+64 = 114

Therefore, 10001110 represents −114