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A series of problems related to 6-bit arithmetic using 2's complement numbers, designing a 4-bit arithmetic block, and creating state diagrams for a moore and mealy machine in digital logic design. Students are required to perform arithmetic operations, design circuits, and create state diagrams using given specifications.
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Perform the following arithmetic using 6 bit 2’s complement numbers. Provide the answer in binary and hexadecimal form.
Design a 4-bit arithmetic block that performs the following functions. You may only use muxes, NOR gates, and 4 full adders. Assme all inputs are 4-bit binary numbers in 2’s complement form.
S 1 S 0 function
0 0 A+B 0 1 A-B 1 0 A+ 1 1 A-
Complete the timing diagram for the following circuit. Assume that the flip-flops have a 2ns delay each and that the XOR gate has a 1ns delay. Both flip-flops are negative edge triggered. Q0 and Q1 are initially high.Assume there are no set-up or hold violations.
An electronic lock is controlled by a keypad that has three buttons labelled A , B , and R. The key- pad is restricted such that, at most, one key can be pressed at a time, and that each keypress gener- ates an input signal that lasts for only one clock cycle. A state machine takes the keypresses as input, and its output is either lock ( L ) or unlock ( U ). If the correct sequence of keys is typed and followed by an R , the state machine generates an unlock ( U ) signal and then resets. At any other time the output should be locked ( L ). If an incorrect sequence of keys is pressed the lock becomes inactive until the reset ( R ) key is pressed, at which point the lock resets (with no unlock signal).
(a) Create state diagram for a MOORE machine that will test for the correct key sequence is BBA. Label your inputs A, B, R, and O (for no key pressed). Label your output L or U. Label your states
1ns Q 2ns 2ns
10ns
