Exam 1 Review
How many full adders would it take to add two 16-bit binary numbers? If you used one half adder, how many full adders would you need? Which column would you use the half adder for?
16 full adders or 15 full adders and on half adder The column used would be the carry.
How many rows are there in a truth table for an expression with n variables?
2^n rows
What is the maximum number of terms in a sum-of-products form could there be?
2^n variables
Why are Boolean identities useful in hardware design?
Because circuits use high and low frequencies which can be interpreted as true or false statements that are evaluated as 0 and 1 and can be used in Boolean logic.
What business decision(s) did IBM make with regard to architecture that made the company so successful?
By using the same architecture, IBM provided an upgrade path Same architecture but not necessarily same hardware design
What is the CPU?
Central Processing Unit that holds registers for fast memory management.
What are the inputs and outputs of a ripple-carry adder? (i.e., draw a black box representation). What does a ripple-carry adder do? What components is it made of?
X, Y, and Carry In are the inputs. Carry Out and Sum are the outputs. It is constructed of Full Adders
What is the difference between a sequential and a combinatorial circuit? Why does a sequential circuit need a clock line?
Combinational circuits produce immediate applications of Boolean functions to a set of Inputs. Sequential circuits require a means by which events can be sequenced. Clock lines will cause state changes whenever the clock "ticks".
What does a decoder do? Draw a black box diagram. What is it useful for?
Decoders are useful in selecting a memory location according a binary value placed on the address lines of a memory bus. Address decoders with n inputs can select any of 2n locations.
Who were Mauchley and Eckert?
Designers of the first general purpose electronic digital computer.
What significant development in computer design did VLSI make possible?
Enabled the creation of microprocessors.
Why can't More's Law hold true forever?
Eventually you'd have transistors smaller than an atom!
What is feedback? Why is it useful?
Feedback in digital circuits occurs when an output is looped back to the input. They are useful to retain their state values.
If an expression has n variables, how many variables will be in each term of the sum-of-products form?
For a function of n variables there will be exactly n items in each of the minterms
Who was Atanasoff?
He solved systems of linear equations. Invented the first electronic digital computer.
Name one or two hardware families where backward compatibility has significantly influenced design.
IBM, Intel, Microsoft
What is sum-of-products form?
It is a form that has terms of variables AND'ed together that are connected by OR statements. F(x,y) = x(!y) + (xy)
Which gates are universal gates?
Only NAND and NOR Gates are universal.
Make sure you know the order of operations for Boolean expressions and the various symbols that can be used.
Parentheses have top priority. NOT has the next priority. AND is next. OR has the lowest priority.
Why are universal gates useful?
Since NAND and NOR are inexpensive to manufacture, this is a useful property.
What is the von Neumann architecture?
Stored-program computers have become known as von Neumann architecture systems.
What is the ALU?
The ALU executes the instruction and places results in registers or memory.
What happens in the step of the fetch cycle?
The control unit fetches the next instruction from memory using the program counter to determine where the instruction is located.
What is Moore's Law?
The density of transistors in an integrated circuit will double every year.
What happens in the step of the decode cycle?
The instruction is decoded into a language that the ALU can understand.
Who was von Neumann?
The invention of a computer that could store instructions in memory has since been ascribed to a mathematician named von Neumann.
Why is the sum-of-products useful?
The purpose of a unique representation is to make it easy to compare two expressions.
What does it mean when there is a 1 in the result column?
The result of the logical operation performed on the given Boolean operators equates to True (aka 1).
Why were transistors an improvement over vacuum tubes?
Transistors more reliable than vacuum tubes
What does VLSI stand for?
Very Large Scale Integrated circuits
What is a clock line? What is the relationship between the clock and state changes in a sequential circuit?
A "clock" is a special circuit that sends electrical pulses through a circuit. State changes occur in sequential circuits only when the clock ticks.
What are the von Neumann architecture's major components?
A central processing unit (CPU) A main memory system An I/O system
What is a stored program computer?
A computer that stores program instructions in electronic memory.
What is a full adder? How is it different from a half adder?
A full adder handles the complete calculation of one column of a binary addition. It has 3 inputs and 2 outputs.
What is a half adder? How many bits can a half adder add?
A half adder is a combinational circuit that finds the sum of 2 bits.
How can you derive the sum-of-products form from the truth table?
A product will be in the sum of products form if and only if the evaluation of the product is true in the truth table
What is the rising edge? falling edge? edge-triggered circuit? level-triggered circuit?
A rising edge is a circuits lower state going to a higher state. A falling edge is a circuits higher state falling to a lower state.
What is a universal gate?
A universal gate means that any Boolean function can be constructed using all NAND gates or all NOR gates.
What happens in the step of the execute cycle?
Any data operands required to execute the instruction are fetched from memory and placed into registers within the CPU.