Chapter 3: Essentials of Computer Organization and Architecture 5th Edition

How many control lines does a multiplexer have if it has 32 inputs?

5 control lines

How many inputs does a decoder have if it has 64 outputs?

6 inputs

What is a combinational circuit?

A circuit that bases their output only on the inputs.

What is a sequential circuit?

A circuit whose output is based on input and the current state of the circuit.

Which Boolean operation is referred to as a Boolean product?

AND

How are sequential circuits different from combinational circuits?

Combinational circuits base their output only on the inputs. Sequential circuits base their output on current state and input. Are usually clock based.

Which flip-flop give a true representation of computer memory?

D flip-flop

What do we mean when we say that a sequential circuit is edge triggered rather than level triggered?

Edge triggered mean that the clock transitions from high to low or low to high. Level is based on the low or high state of the clock.

Using DeMorgan's Law, write an expression for the complement of F if F(x,y,z) = (x'+y)(x+z)(y'+z)'

F(x,y,z) = (x'+y)(x+z)(y'+z)' F'(x,y,z) = ((x'+y)(x+z)(y'+z)')' = (x'+y)'+(x+z)'+(y'+z)'' = xy'+ x'z'+(y'+z) (not simplified)

The truth table for a Boolean expression is shown below. Write the Boolean expression in sum-of-products form. See Image

F(x,y,z) = x'y'z' + x'y'z + x'yz' + xy'z' + xy'z

Describe the operation of a ripple-carry adder. Why are ripple-carry adders not used in most computers today?

Multiple adder as used together with the carry-out of one adder used as an input to the next adder. They are not used because they are too slow.

Which Boolean operation is referred to as a Boolean sum?

OR

Show that x = xy + xy' a) Using truth tables b) Using Boolean identities

a) see image b) x = xy + xy' = x(y + y') Distributive = x(1) Inverse = x Identity

Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step. a) x(y + z)(x' + z') b) xy + xyz + xy'z + x'y'z c) xy'z + x(y + z')' + xy'z'

a) x(y + z)(x' + z') = x(x'y + yz' + x'z + zz') Distributive/Commutative = xx'y + xyz' + xx'z + xzz' Distributive = 0 + xyz' + 0 + 0 Inverse/Null = xyz' Identity b) xy + xyz + xy'z + x'y'z = xy(1 + z) + (x+ x')y'z Distributive = xy(1) + (1)y'z Idempotent = xy + y'z Identity c) xy'z + x(y + z')' + xy'z' = xy'z + xy'z + xy'z DeMorgan = xy'z + xy'(z + z') Distributive = xy'z + xy'(1) Inverse = xy'z + xy' Identity = xy'(z + 1) Distributive = xy'(1) Null = xy' Identity

Construct a truth table for the following: (x + y')(x' + z')(y' + z')

see attached image

Construct a truth table for the following: xyz + x(yz)' + x'(y+z) + (xyz)'

see attached image Note: The last row for SUM should be a 1

Draw the combinational circuit that directly implements the following Boolean expression: F(x,y,z) = x + xy + y'z

see image