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(a) 00001110;

(b) 10001110.

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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

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