Solve each of the following problems. To receive full marks, you must show your

Question

Solve each of the following problems. To receive full marks, you must show your work. In any problem, marks for the sub-problems are equally distributed unless stated otherwise 1. (20 points) Convert the following numbers from the decimal number system to the binary number system: a) 92 b) 511 c) 1000 2. (20 points) Convert the following numbers from the binary number system to the decimal number system a) 101010 b) 101110 c) 110 3. (10 points) Convert the following numbers from the hexadecimal number system to the binary number system a) A03C b) 193F 4. (10 points) How many different numbers can be represented using 8 bits i.e., binary digits)? Give your answer in decimal notation 5. (10 points) What is the largest value (in decimal notation) that can be represented using 11 bits i.e, binary digits)? 6. (10 points) Convert the base-5 number 1011021 into the binary number system. (base-5 number system uses symbols 0, 1, 2, 3, 4) 7. (20 points) Represent the following decimal numbers in 8-bit 2's complement notation. Indicate if the number cannot be represented using 8-bit 2's complement notation. a) -65 b)-129

Explanation / Answer

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1. 92 = 64+16+8+4 = 2^5+2^4+2^3+2^2 = 1011100 <--binary representation

2. 511 = 256+128+64+32+16+8+4+2+1 =2^8+2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0 = 111111111 <--binary representation

3. 1000 = 2^9 +2^8+2^7+2^6+2^5+2^3 = 1111101000 <--binary representation

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