Consider a toy 8-bit floating-point format with a sign bit, a 4-bit exponent fie

Question

Consider a toy 8-bit floating-point format with a sign bit, a 4-bit exponent field, and a 3-bit significand field. Exponents 0000 and 1111 are reserved for special values, and the rest are used to encode exponents -7(0001) and +6(1110). The exponent base is 2. The significand has a hidden 1 to the left of the radix point, with the 3-bit field constituting its fractional part.

a)Represent the numbers x = 0.5 and y = -2 in this format.
b) Compute the sum x + y using the rules of floating-point arithmetic. Show all the steps.

Explanation / Answer

Dear, Binary representation x= 0000 0000.10 y=-2 obtaining 2's complement value we get y= 11111110 x+y= 0000 0000.1 0        1111 1110.0 0        1111 1110.1 0         The 8 bit represents negative sign -1.5                 1111 1110.1 0         The 8 bit represents negative sign -1.5         

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