(Solved): Figure 1 shows a hypothetical floating-point number set for a machine that stores infor- mation usin ...

Figure 1 shows a hypothetical floating-point number set for a machine that stores infor- mation using 6-bit words. The first bit is used for the sign of the number, the next three bits are used for the sign and the magnitude of the exponent, and the last two bits are used for the magnitude of the mantissa. 21 20 21 22 1 1 1 0 0 1 Sign of number Magnitude of Sign of mantissa exponent Magnitude of exponent Figure 1: Floating point number system. Question 1 (10 points) Write down all the (real) numbers represented by the above sys- tem. Question 2 (10 points) Write down how each of the following real numbers will be repre- sented (approximated) by the above system. 1. 0.00 2. 1.5 3. 10.05 4. -3 Show transcribed image text Figure 1 shows a hypothetical floating-point number set for a machine that stores infor- mation using 6-bit words. The first bit is used for the sign of the number, the next three bits are used for the sign and the magnitude of the exponent, and the last two bits are used for the magnitude of the mantissa. 21 20 21 22 1 1 1 0 0 1 Sign of number Magnitude of Sign of mantissa exponent Magnitude of exponent Figure 1: Floating point number system. Question 1 (10 points) Write down all the (real) numbers represented by the above sys- tem. Question 2 (10 points) Write down how each of the following real numbers will be repre- sented (approximated) by the above system. 1. 0.00 2. 1.5 3. 10.05 4. -3