Questions and Answers of Logic And Computer Design Fundamentals

For the CMOS logic family, the power consumption is proportional to the sum of the changes from 1-to-0 and 0-to-1 on all gate inputs and outputs in the circuit. When designing counters in very
(a) Construct a 4-bit up/down counter that uses a Gray-code counting sequence.(b) Repeat Problem 6-9 by comparing the numbers of changing inputs and outputs on the Gray-code counter to a 4-bit
Construct a 16-bit serial-parallel counter, using four 4-bit parallel counters. Suppose that all added logic is AND gates and that serial connections are employed between the four counters. What is
Using two binary counters of the type shown in Figure 6-14 and logic gates, construct a binary counter that counts from decimal 11 through decimal 233. Also, add an additional input and logic to the
Verify the lip-lop input equations of the synchronous BCD counter specified in Table 6-9. Draw the logic diagram of the BCD counter with a count enable input.Table 6-9 0 0 Qs Q Q2 Q 8 0 0 0 0 0 State
(a) Using the synchronous binary counter of Figure 6-14 and an AND gate, construct a counter that counts from 0000 through 1010.(b) Repeat for a count from 0000 to 1110. Minimize the number of
Use D lip-lops and gates to design a binary counter with each of the following repeated binary sequences:(a) 0, 1, 2(b) 0, 1, 2, 3, 4, 5
Draw the logic diagram of a 4-bit register with mode selection inputs S1 and S0. The register is to be operated according to the function table below. S 0 0 1 1 So 0 0 1 0 1 Register Operation No
Use D-type flip-flops and gates to design a counter with the following repeated binary sequence: 0, 2, 1, 3, 4, 6, 5, 7.
Show the diagram of the hardware that implements the register transfer statement C3: R2R1, R1 R2
The outputs of registers R0, R1, R2, and R3 are connected through 4-to-1 multiplexers to the inputs of a ifth register, R4. Each register is 8 bits long. The required transfers, as dictated by four
Using two 4-bit registers R1 and R2, a 4-bit adder, a 2-to-1 multiplexer, and a 4-to-1 multiplexer, construct a circuit that implements the following operations under the control of the three
Using two 4-bit registers R1 and R2, and AND gates, OR gates, and inverters, draw one bit slice of the logic diagram that implements all of the following statements:The control variables are mutually
A register cell is to be designed for an 8-bit register A that has the following register transfer functions:Find optimum logic using AND, OR, and NOT gates for the D input to the D lip-lop in the
A register cell is to be designed for an 8-bit register R0 that has the following register transfer functions:Find optimum logic using AND, OR, and NOT gates for the D input to the D lip-lop in the
Two register transfer statements are given (otherwise, R1 is unchanged):(a) Using a 4-bit counter with parallel load as in Figure 6-14 and a 4-bit adder as in Figure 4-5, draw the logic diagram that
Logic to implement transfers among three registers, R0, R1, and R2, is to be implemented. Use the control variable assumptions given in Problem 6–20. The register transfers are as follows:Using
A register cell is to be designed for register B, which has the following register transfers:Share the combinational logic between the two transfers as much as possible. SO: BB+ A S1: B A + 1
Repeat Problem 6-26 using one multiplexer-based bus and one direct connection from one register to another instead of dedicated multiplexers.Problem 6-26Logic to implement transfers among three
A system is to have the following set of register transfers, implemented using buses:(a) For each destination register, list all of the source registers.(b) For each source register, list all of
(a) Implement function H = X̅Y + XZ using two three-state buffers and an inverter.(b) Construct an exclusive-OR gate by interconnecting two three-state buffers and two inverters.
The following register transfers are to be executed in, at most, two clock cycles: (a) What is the minimum number of buses required? Assume that only one bus can be attached to a register input
What is the minimum number of clock cycles required to perform the following set of register transfers using one bus?Assume that only one bus can be attached to a register input and that any net
The serial adder of Figure 6-24 uses two 4-bit registers. Register A holds the binary number 0111 and register B holds 0101. The carry lip-lop is initially reset to 0. List the binary values in
The content of a 4-bit register is initially 0101. The register is shifted eight times to the right, with the sequence 10110001 as the serial input. The leftmost bit of the sequence is applied first.
A state diagram of a sequential circuit is given in Figure 6-37. Find the corresponding state machine diagram using a minimum amount of notation. The inputs to the circuit are X1 and X2, and the
Find the response for the state machine diagram in Figure 6-38 to the following sequence of inputs (assume that the initial state is STA):Figure 6-38 W: 0 X: 1 Y: 0 State: STA Z: 1 1 1 1 0 0 0 0 1 1
A state machine diagram is given in Figure 6-38. Find the state table for the corresponding sequential circuit.Figure 6-38 Default: Z = 0 W Z- STA W STB RESET X, XY STC XY Z
Find the state machine diagram corresponding to the following description: There are two states, A and B. If in state A and input X is 1, then the next state is A. If in state A and input X is 0,
Find the state machine diagram for a circuit that detects a difference in value in an input signal X at two successive positive clock edges. If X has different values at two successive positive clock
Find a state machine diagram for a trafic light controller that works as follows: A timing signal T is the input to the controller. T deines the yellow light interval, as well as the changes of the
Implement the state machine diagram in Figure 6-38 by using one lip-lop per state assignment.Figure 6-38 Default: Z=0 W N (STA) W RESET (STB) X,XY (STC) XY
The state machine diagram for a synchronous circuit with clock CK for a washing machine is to be developed. The circuit has three external inputs, START, FULL, and EMPTY (which are 1 for at most a
Do two designs for the DIE circuit for the Game of PIG and compare the gate-input costs of your two designs using information from Figure 6-14. Note that the register transfer description of DIE
Design the following combinational circuits for the Game of PIG datapath given in Figure 6-31:Figure 6-31(a) D = 1 comparator.(b) D ≥ 1100100 comparator.Use AND gates, OR gates, and inverters.
Implement the state machine diagram derived in Problem 6-40 by using a Gray-code state assignment.Problem 6-40Find the state machine diagram for a circuit that detects a difference in value in an
(a) Show the details of a check of the constraints given on transition conditions as applied to Figure 6-30.(b) Implement the state machine diagram for the Game of PIG in Figure 6-30 using a
Find the state machine diagram in the form of Figure 6-29 for a Game of PIG using two dice. Also, add the following rule: If a pair of 1s is rolled, then the player’s total score becomes 0. The
Design the 2-digit binary-to-BCD code converter in the datapath for the Game of PIG. Design the least significant digit as a function of (B3, B2, B1, B0)without an incoming carry C0. The outputs are
Write a Verilog description for the 4-bit binary counter in Figure 6-13(a) using a register for the D lip-lops and Boolean equations for the logic. Compile and simulate your description to
Design a digital system with three 16-bit registers AR, BR, and CR and 16-bit data input IN to perform the following operations, assuming a 2s complement representation and ignoring
Write a behavioral VHDL description for the 4-bit register in Figure 6-1(a). Compile and simulate your description to demonstrate correctness.Figure 6-1(a). Do Clock Clear D D D3 D D D D C R R R C
Repeat Problem 6-52 for the 4-bit register with parallel load in Figure 6-2.Figure 6-2Problem 6-52Write a behavioral VHDL description for the 4-bit register in Figure 6-1(a). Compile and simulate
Write a VHDL description for the 4-bit binary counter in Figure 6-13(a), using a register for the D lip-lops and Boolean equations for the logic. Compile and simulate your description to demonstrate
Repeat Problem 6-55 for the 4-bit register with parallel load in Figure 6-2.Figure 6-2Problem 6-55Write a behavioral Verilog description for the 4-bit register in Figure 6-1(a). Compile and simulate
Write a behavioral Verilog description for the 4-bit register in Figure 6-1(a). Compile and simulate your description to demonstrate correctness.Figure 6-1(a). Do Clock Clear D D D3 D D D D C R R R
Write, compile, and simulate a VHDL description for the state machine diagram shown in Figure 6-38. Use a simulation input that passes through all paths in the state machine diagram, and include both
Write, compile, and simulate a Verilog description for the state machine diagram in Figure 6-38. Use code 00 for state STA, 01 for state STB, and 10 for state STC. Use a simulation input that passes
a) Word number (835)10 in the memory shown in Figure 7-2 contains the binary equivalent of (15,103)10. List the 10-bit address and the 16-bit memory contents of the word.(b) Repeat part (a) for
The following memories are specified by the number of words times the number of bits per word. How many address lines and input–output data lines are needed in each case?(a) 48K х 8,(b) 512K х
A 64K х 16 RAM chip uses coincident decoding by splitting the internal decoder into row select and column select.(a) Assuming that the RAM cell array is square, what is the size of each decoder,
Assume that the largest decoder that can be used in an m х 1 RAM chip has 14 address inputs and that coincident decoding is employed. In order to construct RAM chips that contain more one-bit words
A DRAM has 15 address pins and its row address is 1 bit longer than its column address. How many addresses, total, does the DRAM have?
A 4 GB DRAM uses 4-bit data and has equal-length row and column addresses. How many address pins does the DRAM have?
A DRAM has a refresh interval of 64 ms and has 8192 rows. What is the interval between refreshes for distributed refresh? What is the total time required out of the 64 ms for a refresh of the entire
Using the 64K х 8 RAM chip in Figure 7-9 plus a decoder, construct the block diagram for a 1M х 32 RAM.Figure 7-9 Input data- Address Chip Select- Read/Write 8 16 + 64K X 8 RAM DATA ADRS CS R/W 8
(a) How many 128K х 16 RAM chips are needed to provide a memory capacity of 2 MB?(b) How many address lines are required to access 2 MB? How many of these lines are connected to the address inputs
A datapath similar to the one in Figure 8-1 has 64 registers. How many selection lines are needed for each set of multiplexers and for the decoder?Figure 8-1 Load enable Write D data 0123 Decoder D
Explain how SDRAM takes advantage of the two-dimensional storage array to provide a high data access rate.
Design an arithmetic circuit with two selection variables S1 and S0 and two n- bit data inputs A and B. The circuit generates the following eight arithmetic operations in conjunction with carry
Given an 8-bit ALU with outputs F7 through F0 and available carries C8 and C7, show the logic circuit for generating the signals for the four status bits N (sign), Z (zero), V (overflow), and C
Design a 4-bit arithmetic circuit, with two selection variables S1 and S0, that generates the arithmetic operations in the following table. Draw the logic diagram for a typical single- bit stage and
Inputs Xi and Yi of each full adder in an arithmetic circuit have digital logic specified by the Boolean functionswhere S is a selection variable, Cin is the input carry, and Ai and B i are input
Design an ALU that performs the following operations:Give the result of your design as the logic diagram for a single stage of the ALU. Your design should have one carry line to the left and one
Design one bit of a digital circuit that performs the four logic operations of exclusive- OR, exclusive- NOR, NOR, and NAND on register operands A and B with the result to be loaded into register A.
Specify the 16-bit control word that must be applied to the datapath of Figure 8-11 to implement each of the following microoperations:Figure 8-11 Data in sr R4 sl R2 (a) R3 (c) R1 (e) R2 (g) R7R1 +
Given the sequence of 16-bit control words below for the datapath in Figure 8-11 and the initial ASCII character codes in 8-bit registers, simulate the datapath to determine the alphanumeric
Find the output Y of the 4-bit barrel shifter in Figure 8-9 for each of the following bit patterns applied to S1, S0, D3, D2, D1, and D0:(a) 110101(b) 101011(c) 011010(d) 001101
Given the following 16-bit control words for the datapath of Figure 8-11, determine (a) the microoperation that is executed and (b) the change in the contents of the register for each control word
The single- cycle computer in Figure 8-15 executes the ive instructions described by the register transfers in the table that follows.Figure 8-15(a) Complete the following table, giving the binary
List the control logic state table entries for the multiple- cycle computer (see Tables 8-12, 8-13 and 8-15) that implement the following register transfer statements. Assume that in all cases the
Using the information in the truth table in Table 8-10, verify that the design for the single- bit outputs in the decoder in Figure 8-16 is correct.Table 8-10Figure 8-16 Truth Table for Instruction
A computer has a 32-bit instruction word broken into ields as follows:opcode, six bits; two register ile address ields, ive bits each; and one immediate operand/register ile address ield, 16
Manually simulate the single- cycle computer in Figure 8-15 for the following sequence of instructions, assuming that each register initially contains contents equal to its index (i.e., R0 contains
A digital computer has a memory unit with a 32-bit instruction and a register file with 64 registers. The instruction set consists of 130 different operations. There is only one type of instruction
A digital computer has 32-bit instructions. There are a number of different instruction formats, and the number of bits in each format used for opcodes varies depending on the bits needed for other
Give an instruction for the single- cycle computer that resets register R4 to 0 and updates the Z and N status bits based on the value 0 transferred to R4.By examining the detailed ALU logic,
a) Manually simulate the SRM (shift right multiple) instruction in the multiple- cycle computer for operand 0101100111000111 for OP = 5.(b) Repeat part (a) for the SLM (shift left multiple)
Repeat Problem 8-22 for the two instructions: Add and check OV (AOV), described by the register transferand branch on overlow (BRV), described by the register transferThe opcode for AOV is 1000101
A new instruction is to be deined for the multiple- cycle computer with opcode 0010001. The instruction implements the register transferFind the state machine diagram for implementing the
In the SRM and SLM instructions, both the operand R[SA] and the shift amount ield OP are checked to see if either is 0 before the shifts begin.(a) Redraw the state machine diagram for these
A new instruction, SMR (Store Multiple Registers), with symbolic opcode name SMR, is to be implemented for the multiple- cycle computer. The instruction stores the contents of eight registers in
A new instruction is to be defined for the multiple- cycle computer. The instruction compares two unsigned integers stored in register R[SA] and R[SB]. If the integers are equal, then bit 0 of R[DR]
A new instruction, ANDN (AND NOT), is to be implemented for the multiple-cycle computer. The instruction performs R[DR] = R[SA]^(NOT(R[SB])). The instruction allows individual bits in register SA to
A program is to be written for a stack architecture for the arithmetic expression(a) Find the corresponding RPN expression.(b) Write the program using PUSH, POP, ADD, MUL, SUB, and DIV instructions
Repeat Problem 9-3 for the arithmetic expressionProblem 9-3A program is to be written for a stack architecture for the arithmetic expression(a) Find the corresponding RPN expression.(b) Write the
Using the instructions for the single- cycle computer, write a program that reads through an array of 16-bit signed 2s complement numbers stored in data memory and finds the minimum value in the
A two- word relative mode branch- type instruction is stored in memory at locations 207 and 208 (decimal). The branch is made to an address equivalent to decimal 195. Let the address field of the
Repeat Problem 9-6 for a branch instruction in locations 143 and 144 and a branch address equivalent to 1000. All values are in decimal.Problem 9-6A two- word relative mode branch- type instruction
How many times does the control unit refer to memory when it fetches and executes a three- word instruction using two indirect addressing- mode addresses if the instruction is(a) A computational
An instruction is stored at location 550 with its address field at location 551. The address field has the value 2410. A processor register R1 contains the number 2310. Evaluate the effective address
A computer with a register ile, but without PUSH and POP instructions, is to be used to implement a stack. The computer does have the following register indirect addressing modes:Show how these
Assume a computer with 8-bit words for the multiple- precision addition of two 32-bit unsigned numbers,(a) Write a program to execute the addition, using add and add with carry
A computer with an independent I/O system has the input and output instructionswhere ADRS is the address of an I/O register port. Give the equivalent instructions for a computer with memory- mapped
An 8-bit register contains the value 01101001, and the carry bit is equal to 1. Perform the eight shift operations given by the instructions listed in Table 9-5 as a sequence of operations on this
A computer has a 32-bit word length, and all instructions are one word in length. The register ile of the computer has 16 registers.(a) For a format with no mode ields and three register addresses,
A complex instruction, push registers (PSHR), pushes the contents of all of the registers onto the stack. There are eight registers, R0 through R7, in the CPU. A corresponding instruction, POPR, pops
(a) Perform the logic AND, OR, and XOR with the two bytes 01101001 and 11001110.(b) Repeat part (a) with the two bytes 01010001 and 00111001.
Given the 16-bit value 1010 0101 1001 1000, what operation must be performed, and what operand is needed, in order to(a) The most significant 8 bits to 1s?(b) The bits in even positions (the
Show how the following two floating- point numbers are to be added to get a normalized result: (-.12345 10+5) + (+.71234 10-) X

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