CS 1400 Computer Organization Final Exam B Type 900 ✓ Solved

Cs 1400 Computer Organization Ifinal Exam B Type 900 I

Identify your student ID number (900#). Use the last two digits of your 900 number as a decimal number and convert it to binary representation. For example, if the last two digits are 11, the binary representation is 1011; if they are 01, the binary is 1.

Explain why, in binary numeral system, 7 bits are needed to represent the decimal value 64.

Describe the differences between open loop and closed loop data transfer approaches between a processor and peripheral device.

Simplify the Boolean expression, showing all steps. You are not awarded points for only providing the final simplified answer.

Convert the given Boolean expression to a product of sums using de Morgan's theorem. Show all steps involved in the conversion.

Given a truth table for inputs A, B, and C with output F, derive the Boolean expression for F as a sum of minterms. Then, simplify this expression and draw the corresponding circuit using basic gates.

Explain the difference between a D latch and a D flip-flop. Additionally, discuss whether a D latch can be used to make a falling edge triggered D flip-flop, providing an explanation of how a D flip-flop can be constructed from D latches.

In a counter built with JK flip-flops triggered on the negative edge, initial states are all set to 1. Sketch the output waveforms Q2, Q1, Q0 over time, labeling the binary output value at each clock period. Describe the function of the counter (e.g., binary down counter from 7 to 0).

For a MIPS CPU with an ALU controlled by a 3-bit control signal, determine the control signal values required for the 'sw' instruction (store word) and 'addi' instruction. If the 'MemWrite' control signal is stuck at 0, identify which instructions will fail to execute correctly and explain why.

Sample Paper For Above instruction

Introduction

Computer organization is fundamental to understanding how hardware components interact to perform computing tasks. This paper addresses central concepts of digital logic, data transfer mechanisms, sequential logic devices, and processor control signals within the context of a typical computer architecture course, specifically CS 1400. The exploration includes Boolean algebra, logic circuit design, flip-flop operation, counters, and MIPS processor control mechanisms, offering a comprehensive overview suitable for students aiming to demonstrate mastery of foundational computer engineering principles.

Binary Representation and Data Transfer Mechanisms

Binary representation is critical in digital systems, reflecting how data are processed at the hardware level. To represent decimal value 64 in binary, 7 bits are necessary. This requirement stems from the fact that 7 bits can encode integers from 0 to 127 (2^7 - 1). Since 64 is within this range, it can be represented as 1000000 in binary. The most significant bit (MSB) in this case signifies 2^6, which equals 64 when set to 1, with all other bits zero. This demonstrates why 7 bits are needed to encode the number 64 uniquely in binary form.

Data transfer between the processor and peripherals can occur in open loop or closed loop modes. Open loop transfer involves unidirectional data flow where the sender transmits data without regard to the receiver's acknowledgment, typical in simple data streaming. Conversely, closed loop transfer incorporates feedback mechanisms and handshaking protocols, ensuring data integrity through acknowledgments and error checking, commonly used in reliable communication channels. The primary distinction lies in error handling and synchronization: open loop lacks feedback and is faster but less reliable, while closed loop emphasizes correctness over raw speed.

Boolean Algebra Simplification and Circuit Design

Boolean algebra allows us to simplify logical expressions to optimize digital circuit designs. For example, consider the expression (AB + A'B' + A'B). Utilizing Boolean theorems, such as the consensus theorem and de Morgan's theorem, the expression simplifies to B + A'. This reduction results in a more efficient implementation using fewer gates. The process involves systematically applying Boolean identities: first, grouping terms, then using the distributive, absorption, and de Morgan's laws to minimize the expression. The simplified form directly translates into a logic circuit that is cost-effective and faster.

Another example involves converting a Boolean expression into product of sums (POS) form. Starting with the expression (A + B)(A' + C), one can verify using de Morgan's theorem that it represents a function minimized for implementation. This conversion aids in designing gates like NOR gates for specific logic functions, as POS form often aligns well with NOR-based logic synthesis, further optimizing the hardware design.

Design and Operation of Logic Gates and Sequential Devices

The truth table provided depicts a combinational logic circuit whose Boolean function can be expressed as a sum of minterms. For each minterm where the output is 1, the corresponding Boolean product term is written. After deriving the sum of minterms, the Boolean expression can be simplified using Karnaugh maps or algebraic methods to yield a minimal expression, which is then implemented with AND, OR, and NOT gates. The actual circuit diagram visualizes the connections of these gates, offering a tangible understanding of logical operations.

Sequential logic devices like latches and flip-flops serve as memory elements within digital circuits. A D latch is transparent during enable, allowing input signals to pass directly to the output, functioning as a level-sensitive device. Conversely, a D flip-flop is edge-triggered, changing state only at a specific clock transition (rising or falling). The primary difference lies in their sensitivity: latch operation depends on enable level, while flip-flop operation depends on clock edges. A D latch can be combined with additional logic to construct a falling edge triggered flip-flop by synchronization circuitry, though practical circuits often employ master-slave arrangements for this purpose.

Counter Design Using JK Flip-Flops

JK flip-flops, configured with both J and K inputs tied high, toggle their state on each clock pulse. In a negative edge-triggered counter with initial states of Q2Q1Q0 as 111, the waveforms can be visualized over successive periods. The outputs change according to the counter's counting sequence, such as binary down counting from 7 to 0. The logic of the counter involves cascading flip-flops where the toggle condition depends on the states of lower bits, implementing counting sequences necessary for applications like timers, dividers, and state machines.

MIPS Processor Control Signals and ALU Operations

The MIPS architecture employs control signals to direct the ALU for various instructions. For the 'sw' (store word) instruction, the control signals would typically set the ALU to perform addition to compute memory addresses, with MemWrite enabled to allow writing to memory. For 'addi', the control signals would configure the ALU to add an immediate value to register contents, with appropriate control signals set accordingly. If the 'MemWrite' control signal is stuck at 0, all store operations ('sw') would fail because the processor would not write data to memory, highlighting the importance of correct control signal operation in instruction execution.

In particular, the control signals for 'sw' involve setting ALU operation to addition and enabling memory write (MemWrite=1). For 'addi', the ALU must perform addition with immediate data, and memory write remains disabled. The fault disrupts store operations, which rely on MemWrite being active, thus causing memory storage to fail during 'sw' execution, while load and register operations ('lw', 'add', 'addi') would continue normally, assuming no other faults.

Conclusion

This comprehensive analysis of fundamental digital logic concepts solidifies understanding necessary for designing and analyzing computer architectures. Mastery of binary representations, Boolean algebra, sequential circuits, and control logic is crucial in computing systems. Such knowledge underpins efficient hardware design and optimization, aligning with the goals of courses like CS 1400 to prepare students for advanced studies or careers in computer engineering and systems design.

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