28. 3.28 Derive the circuits for a three-bit parity generator and a four-bit parity checker using an odd-parity bit.

parity generator design, construct and test a circuit that generates an even parity bit ffrom four messages bits . use XOR gates. adding one more XOR gate, expand the circuit so that it generates an odd parity bit also.

Up/Down State Machine Cousider a state machine implementation of a two bit up/down counter mput: up/doun, and two outputs: Outo and Out,, which also indicate the next state. When up/dowTI is high, the counter counts up (00,01,10,11,00, ). When up/doun is low, the counter counts down (00,11.10.01.00, ..). The state machine has one Part A Complete the state diagram below by adding all required transition arcs with input annotations. Output annotations are not required since they correspond to the new state. state state 00 01 state state 10 11

Design the following combinational logic circuit with a four-bit input and a three-bit output. The input represents two unsigned 2-bit numbers: A1 A0 and B1 B0. The output C2 C1.C0 is the result of the integer binary division A1 A0/B1 B0 rounded down to three bits. The 3-bit output has a 2-bit unsigned whole part C2 C1 and a fraction part CO. The weight of the fraction bit CO is 21. Note the quotient should be rounded down, i.e. the division 01/11 should give the outputs 00.0 (1/3 rounded down to 0) not 00.1 (1/3 rounded up to 0.5). A result of infinity should be represented as 11.1. A minimal logic implementation is not required. (Hint: start by producing a truth table of your design).