ECE 171 DUT 2012 Homework 1 1. [5] Use the “subtract the weights” or “repeated radix division” method to convert each of the following decimal integers to binary. Show your work. a) 14 b) 36 c) 47 d) 78 e) 156
2. [5] Convert each of the following binary numbers to its equivalent hexadecimal representation using the “groups of 4” method. a) 01110011 b) 10000101 c) 00111100 d) 10111110 e) 11101111 3. [5] Convert each of the following hexadecimal numbers to its equivalent binary representation using the “groups of 4” method in reverse. a) A b) 2B c) 16 d) BEEF e) CAFE 4. [10] Convert each of the following binary numbers to its equivalent octal and hexadecimal representations. a) 10000001 b) 101010100 c) 10001000.101 d) 1100001.1 e) 110101.11 5. [5] Convert each of the following hexadecimal numbers to its decimal equivalent using the polynomial function method. a) 2116 b) 2B16 c) D116 d) EE16 e) 7C16 6. [5] Fill in the table below 20 21 22 23 24 25 26 27 28 29 210 Decimal Binary Octal Hexadecimal 7. [5] Construct a table showing the hexadecimal numbers between 00 and 20 and their corresponding binary equivalents. 8. [6] Convert the decimal number 0.625 to its binary, octal, and hexadecimal equivalents. 9. [6] Convert the decimal number 13.9 to its binary, octal, and hexadecimal equivalents. Show your work. For two digits for the fractional part of the octal number. ECE 171 DUT 2012 Homework 2 1. [10] Assume each of the following binary numbers is a twos complement (radix complement) representation. Convert each to its decimal equivalent. a) 00101011 b) 11001011 c) 00101.101 d) 11011.101 e) 10001.011 2. [15] Write each of the following decimal numbers in binary signed magnitude (SM),ones complement (DRC – diminished radix complement), and twos complement (RC – radix complement) using a word size of 8 bits. a) 24 b) 42 c) – 16 d) – 37 e) – 10 3. [10] Perform each of the following arithmetic operations in both decimal and twos complement. Use a word size of 8 bits for the twos complement representations. Use indirect subtraction by addition rather than subtraction for the subtraction problems. a) 12 + 7 b) 11 + (– 3) c) –20 – (–6) 4. [5] What is overflow? 5. [5] How do you detect overflow when adding unsigned binary (UB) numbers? 6. [5] How do you detect overflow when adding twos complement (radix complement) numbers? 7. [5] A disk drive interface provides a 32-­‐bit register to specify the address of a block of storage. How many unique addresses can there be? If each disk block contains 512 bytes, what is the maximum capacity (in bytes) of a disk using this interface? 8. [5] Write the binary code and hexadecimal equivalent for the ASCII character ‘F’. 9. [5] A block diagram for an analog to digital converter is shown below. The device converts an analog signal (a voltage) on its input into a binary number on its outputs. The resolution of the LSB, the full scale range of the input voltage (VFSR), and the number of bits (n) are related as follows: Resolution of LSB = VFSR/2n. How many bits are required if the full scale voltage range is 6V and the resolution of the LSB is 1mV? 10. [15] What decimal number is represented by C203000016 assuming it represents a number in IEEE 754 floating point format? Show your work.