Fixed-point numbers A fixed-point binary number system has \'m\' whole bits and
ID: 3798246 • Letter: F
Question
Fixed-point numbers A fixed-point binary number system has 'm' whole bits and 'n' fractional bits. What is the range of numbers represented, assuming an unsigned format? Does every binary rational in this range have a finite decimal expansion?____ (yes/no) Justify your answer. A fixed-point binary number system has 4 whole bits and 12 fractional bits. Represent the decimal fractions 0.75, 0.3, and 1/20 in this format. Recipe: Deal with the integer part separately Now take the fractional part, multiply by 2, record the integer part as one digit of your answer, and repeat until the fractional part is 0, or you run out of binary digits. Practice on 0.6875 11/16 = (0000.101100000000) --- or just (0.1011). Do not round. For grading, also show the answers in hexadecimal.Explanation / Answer
a) Assuming an unsigned format, range of numbers represented is 2^(m+n)-1.
Yes, the range will have a finite expansion, depending on the number of bits we are representing.
b) 0.75 is represented as 0000.110000000000 in given fixed point binary format and 0000.C00000000000 in hexadecimal format
0.3 is represented as 0000.010011001100.. in given fixed point binary format and 0000.4CCCCCCCCCCC in hexadecimal format
1/20 is represented as 0000.000010100011.. in given fixed point binary format and 0000.0A3D70A3D70A in hexadecimal format
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