Show how the following decimal numbers are stored as signed binary integers in a
ID: 3862583 • Letter: S
Question
Show how the following decimal numbers are stored as signed binary integers in a digital system. The system uses 2's complement representation, and has a word size of 12 digits. a) 152 b) -302 c) -4096 d) -128 ii) Convert the above numbers (a-d) to HEX (hexadecimal). Perform the following base conversions (do not exceed 4 digits in your answers after the radix point) of unsigned numbers: a) (FED6.A8)_16 = ()_8 b) (110101.1101)_2 = ()_16 c) (32.42)_8 = ()_18 d) (CD.12)_16 = ()_2 Convert the following numbers as indicated (show steps of calculation): a)(1011011101001101100)_2 = ()_16 b) (E288)_16 = ()_10 c) (7675)_10 = ()_16 d) (3CD.25)_14 = ()_6 Given that a CPU uses 12 bits to represent integer numbers, perform the following operations where, X = E01 and Y = FA2. Note that negative numbers are represented using 2's complement system. State your answer in binary and decimal forms and state if there is an overflow or not: i) a) P = X -Y b) Q = Y-X c) R = X + Y ii) Check and show your results by doing the arithmetic in decimal for both cases. Add, subtract and multiply in binary the following numbers, giving results in a table: a) 1101 and 101 b) 101010 and 11010 c) 100100 and 1101 Given A = (122)_10 and B = (5)_10, carry out the following operations in unsigned binary: a) C = A/B b) D = A*B What is the binary code for the following message given that 7-bit ASCII is used for packet transmitted using odd parity scheme for 1-bit error detection? Assume a parity bit precedes each ASCII character code: name@org.tr You are required to construct a table for an arbitrary "4 2 3 1" weighted code for decimal digits 0 9. Show the unused bit combinations. Show how you would represent 3856 using this code? Simplify the following Boolean expressions to a minimum number of literals i) yx'z' + xyz' + x'y'z' + z' x ii) (y + x' + z) (z + y + z) iii) (y + x) (x' + y')' i. Given the function F(, B, C) = Product M(0, 2, 5, 7): a) Find a minimal SOP expression, b) Find a minimal POS expression. ii. a) Find all the maxterms of f(w, x, y, z) = wy'z' + x'(w' + z), and express it in maxterm expansion form: f(w, x, y, z) = Product M(?) b) Obtain the minterm expansion for f(w, x, y, z).Explanation / Answer
1.
a) 152 = 000010011000
b) -302 = 111011010010
c) - 4096 = 1000000000000
d) -128 = 111110000000