Converting binary number , the class is digital design

Perform the following conversions: a. 456.14 in Octal to Decimal b. 1000.7 in Decimal to Hexadecimal c. [login to view URL] Hexadecimal to Octal d. 11011.011 in Binary to Octal 2. Simplify the following: a. xyz + x’y + xyz’ b. ABC + A’B + ABC’ c. (x + y)’ (x’ + y’) 3. List the truth table of the following functions. Also draw the logic diagram (gate implementation of the following functions) a. F = xy + xy’ + y’z b. Y = (A + B) (C’ + D) 1. Write the canonical sum of products and canonical product of sums for the following functions: a. F = ΣX,Y,Z(0,3) b. F = ΠA,B,C(1,2,4) 2. Write Verilog code to describe the following functions: a. f1 = x1x3’ + x2x3’ + x3’x4’ + x1x2 +x1x4’ b. f2 = (x1 + x3’) . (x1 + x2 + x4’) . (x2 + x3’ + x4’) 3. A given system has 3 sensors that can produce an output of 0 or 1. The system operates properly when exactly one of the sensors has its output equal to 1. An alarm must be raised when two or more sensors have the output of 1. Design the simplest circuit that can be used to raise the alarm. Use K-MAP for the simplest circuit. 4. • Perform the following operations involving eight-bit 2’s complement numbers and indicate whether arithmetic overflow occurs. Check your answers by converting to decimal sign-and-magnitude representation. o 00110110 - 01000101 o 01110101 + 11010110 • Given two binary numbers X = 1010100 and Y = 1000011, perform the subtraction. o X – Y o Y – X • Write Institute of Electrical and Electronics Engineers (IEEE) floating point representation (32 bits) of the following: o Decimal number 100.75 o 1 01100000 11000000000000000000000