Logical operations can be performed on strings of bits by considering each pair of corresponding bits separately (this is called bitwise operation). Given two 8-bit strings A = 10101101 and B = 10001110, evaluate the 8-bit result after the following logical operations: (a) AND, (b) OR, (c) XOR, (d) NOT A, (e) NOT B. %3D
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- Convert the following pairs of decimal numbers to 6-bit, signed 1's-complement binary numbers and add them. State whether or not overflow occurs in each case. (Please show the steps as we did in Lecture 2. You may not get points by just simply stating overflow or not) a) 8 and 23 b) -8 and 23 c) 18 and -23 d) -18 and -23 Repeat Problem #1 for 7-bit, signed 2's-complement binary numbers.(c) A 4-bit ripple adder has inputs 1101 and 1001, and carry in = 0. What would the output of the adder including the carry out? If the inputs are considered as signed numbers using 2's complement representation, explain briefly whether there has been an overflow or not.Q1 Count in Octal from 0 to 22. Q2 Convert (10010100011), to Hexadecimal. Q3 Express the decimal number (- 35) as an 8-bit number in 2's complement form.
- A logic function is expressed by the equation = 0.1.8.9.4. Plot the the values on the K-map below Note: w is the msb (most significant bit) 3 x 10 0- - W X 1 00 01 Write the simplified Sum of Products (SOP) expression. Use yz WIM or "" for NOT; 11 10 for AND; "+" for OR (without the quotation marks.1. Gray code to Binary converter: Gray code is one of the codes used in digital systems. It has the advantage over binary numbers that only one bit in the code word changes when going from one number to the next. (See Table 1). Design a combinational circuit with 4 inputs and 4 outputs that converts a four- bit gray code number into an equivalent four-bit Binary number. Use Karnaugh map technique for simplification. Use LogicWorks for pre-lab demonstrations. Select the library "7400dev.clf* in the Parts Palette and then select the XOR chip 74-86. This would give you a set of 4 XOR's as shown in Fig. 1, just like the hardware chip 74-86. You could use as many as needed from these XOR gates in your design. Get back to ALL LIBRARIES and select switches for the inputs and Binary Probes as indicators of the outputs. Verify your design in the pre-Lab. During the Lab construct the circuit and verify its operations.Subtract the following 16-bit binary numbers. a. 11001011 00101000. - 10011110 01011011, b. 10111100 10111000, - 10011000 111100112
- Grey converters are often used in industrial circuits where the normal sequence of binary numbers may produce ambiguity during transition. This is elliminated with the Grey code, as only one bit changes, during a normal transition of sequential numbers. Show the logic required to convert a 10-bit binary number to Gray code and use that logic to convert the following to Gray code: a) 1010101010 b) 1111100000 c) 0000001110 d) 1111111111Design a binary multiplier that multiplies two 8-bit binary number by following design rules thatshown in class. The Q and B are the two separate 8-bit binary inputs, C is the 3-bit sequence counterand R is the 16-bit result. (Note: Explain the registers that you will use to establish given process.) The steps are writing algorithm Drawing circuit undetailed (Just use the box, which have only writin under that their functions) Draw logic circuits one by one showing the internal structure of the boxes. Mahe flow chards for registersQ1) Do as required. a) Express decimal number (-123) in binary as an 8-bit sign-magnitude form. b) Add the BCD numbers: 10011000 + 10010111
- From the function below; try solve this by karnaugh map. 1. how many output variables there are?2. what is the value of entry #3 if A is the most significant bit and C is the least significant bit?3. find the minimum function in the sum of products using karnaugh mapSimplify the expression f (A,B,C,D) = Sm (0,1,4,8,9,12,14,15) using K– map and realize the final expression using basic logic.What parity bit, P, should be added to the following data if the parity is EVEN? If the parity is ODD? a. 1111100 b. 1010110 c. 0001101