131 Week 4 - Arithmetic Logic Unit

Question 1

Role of the arithmetic logic unit (ALU)

Answer 1

Implements arithmetic (add, subtract, shifts etc) and logic operations (and, or, not, xor; comparisons - < = > etc.)

Question 2

What does the ALU provide

Answer 2

Registers and status flags

Question 3

Half adder

Answer 3

A logic circuit for adding 2 bits and returning a sum bit and carry bit.
XOR for sum and AND for carry.

Question 4

Full adder

Answer 4

A logic circuit for adding 3 bits (2 inputs and 1 carry input) and returning a sum bit and carry out bit.

Question 5

Ripple carry adder

Answer 5

Full adders can be connected together by linking C out of previous adder and C in of current adder allowing them to add multi bit numbers.

Question 6

Disadvantage of ripple carry adder

Answer 6

They are slow because each full adder relies on the C out of the previous adder meaning each adder has to be executed one after another.

Question 7

Carry select adder

Answer 7

Connects carry bits of adders similar to a ripple carry adder.
Lower half of the bits are added like a ripple carry adder.
Upper half of the adder is added twice, once assuming the first C in is 0 and another assuming it is 1.
After the lower half of the bits has been added, the correct prediction of the upper half of the bits is selected and an output is returned.

Question 8

Advantages of a carry select adder

Answer 8

Because all 3 additions can be executed in parallel, a carry select adder is effectively twice as fast as a ripple carry adder.

Question 9

Status flag

Answer 9

Bits organised into a special register called the flags register.
Each flag reflects an aspect of the result of an ALU operation.

Question 10

Zero flag

Answer 10

Checks if an output results in 0.
Works by using a NOR gate on the result of an operation:
If any of the results of an ALU operation is 1, the zero flag is 0.
If all results of an ALU operation is 0, the zero flag is 1

Question 11

Negative flag

Answer 11

Checks if an output results in a negative number.
Works by checking if the leftmost bit is 1 or 0:
If it is 1, the number is negative.
If it is 0, the number is positive.

Question 12

Overflow flag

Answer 12

Checks if an output has resulted in an overflow error.
Works by checking signs of the inputs and the result.
If positive + positive = negative or negative + negative = positive, an overflow error has occurred.

Question 13

Logic circuit for overflow flag

Answer 13

C in XOR C out

Question 14

Bit shifting

Answer 14

A bit shift left or right works as multiplying or dividing by a power of 2 respectively.

Question 15

4 types of shifts

Answer 15

arithmetic shift, logical shift, rotate and rotate through carry