Study the following 9 bit number: 010001111The number format is fixed-point with 5 bit integer, 4-bit fraction, two's complement. Convert this to decimal. Use up to 4 decimal places (round if necessary)
Question
Study the following 9 bit number: 010001111The number format is fixed-point with 5 bit integer, 4-bit fraction, two's complement. Convert this to decimal. Use up to 4 decimal places (round if necessary)
Solution
The given 9-bit number is 010001111.
The number format is fixed-point with 5-bit integer and 4-bit fraction in two's complement.
The 5-bit integer part is 01000, which is 8 in decimal.
The 4-bit fraction part is 1111. To convert this to decimal, we consider each bit as a negative power of 2. So, 1111 in binary is 1*(1/2) + 1*(1/4) + 1*(1/8) + 1*(1/16) = 0.5 + 0.25 + 0.125 + 0.0625 = 0.9375 in decimal.
So, the given 9-bit number 010001111 in fixed-point with 5-bit integer and 4-bit fraction in two's complement is 8.9375 in decimal.
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