Chapter 2

Question 1

What numerical system is used to store all information in a microprocessor? And in computing datasheets?

Answer 1

Respectively the binary and hexadecimal systems.

Question 2

What is the simplest type of data number in binary?

Answer 2

Unsigned integers.

Question 3

How many unique combinations can N bits represent for unsigned integers? For signed integers?

Answer 3

They can both represent 2^n integers, however the range differs:
- Unsigned integers : [0, 2^n - 1]
- Signed integers: [ -2^(n-1), 2^(n-1) - 1]

Question 4

How do you determine the binary code of a negative integer in the two’s complement system?

Answer 4

You first need to take the one’s complement by inverting all the bits, and then add 1 to the result.

Question 5

What does the Most Significant Bit (MSB) represent in two’s complement encoding?

Answer 5

The MSB is the sign bit:
- 0 = positive number
- 1 = negative number

Question 6

What is a fixed-point number system?

Answer 6

System where some of the binary digits represent the numbers before the binary point, and some after.
Where the binary point occurs exactly has to be agreed by the creator and user of the fixed-point number.

Question 7

What system allows very large or small numbers to be represented with high accuracy in binary?

Answer 7

Floating point number system; it is comparable to scientific notation, several digits can exist after the decimal point to increase accuracy and the use of the exponent.

Question 8

What is Binary Coded Decimal (BCD)?

Answer 8

Numeration system where 4 bits are used to encode each decimal digit (0-9).

Question 9

How is text information stored in binary?

Answer 9

Using encoding schemes: encoding each character using ASCII, Unicode…

Question 10

What does ASCII use to encode characters?

Answer 10

Simplest scheme: uses 7 bits to encode letters of the western alphabet and various other symbols.

Question 11

What is Unicode? How does it differ from ASCII?

Answer 11

More complex scheme: uses up to 32 bits, and currently encodes around 110,000 different characters.
It is able to encode different alphabets and technical symbols —> lots more beyond the ASCII characters.

Question 12

What is the difference between upper- and lower-case letters in ASCII encoding?

Answer 12

To convert from an uppercase character ASCII code to its lowercase equivalent, we add Ox20 (hexadecimal) = we flip the 6th bit.

Question 13

How are Boolean true/false values represented in binary?

Answer 13

1 = True
0 = False

Question 14

What is a data word in a microprocessor?

Answer 14

A block of bits used to store a number, typically 8, 16, 32, or 64 bits.

Question 15

What is the word size of the PIC 16F884A microprocessor?

Answer 15

8 bits (a byte).

Question 16

What happens if a word size is too large or too small for the data?

Answer 16

Too large: the extra bits will be 0 – essentially unnecessary.
Too small: the word cannot represent the full value of the data, additional bits are needed.

Question 17

How do you extend a signed integer to fit a larger word size? And an unsigned integer?

Answer 17

Signed integer: repeat the Most Significant Bit (MSB) to fill the additional bits.
Unsigned integer: add leading zeros to fill the additional bits.

Question 18

What are the two forms of the right shift instruction in the MIPS architecture?

Answer 18

1) Shift Right Logical: Replaces the vacant bit with 0 (zero-extension).
2) Shift Right Arithmetic: Repeats the original MSB (sign-extension).

Question 19

To what mathematical operation is a right shift equivalent? And shift left?

Answer 19

With unsigned integers:
Shift right = division by 2
Shift left = multiplication by 2

Question 20

What is word-addressable memory?

Answer 20

Each memory address corresponds to a word of data.

Question 21

What is byte-addressable memory?

Answer 21

Each memory address corresponds to a single byte of data.

Question 22

What is endian-ness in microprocessors? How does it work (name 2 systems)?

Answer 22

The order in which bytes are stored in memory:
- Little-endian memory stores the least-significant / littlest byte at the lowest memory address.
- Big-endian memory stores the most-significant byte at the first / lowest memory address.

Question 23

How can endian-ness cause problems?

Answer 23

Data transfer between systems with different endian-ness can lead to misinterpretation of byte order.

Question 24

What are status flags?

Answer 24

Special bits in the Status Register that provide information about the previous process in the ALU.

Question 25

What does the Zero (Z) flag indicate?

Answer 25

It is set to 1 if the result of the previous calculation is zero.

Question 26

How is the Zero flag calculated?

Answer 26

It is the NOR of every bit in the result.

Question 27

What does the Carry (C) flag indicate?

Answer 27

It is set to 1 if the result cannot fit within the allowable bits or during subtraction if there is a borrow.

Question 28

What does the Overflow (V) flag indicate?

Answer 28

It is set to 1 if the result of an operation on signed integers exceeds the range that can be represented.

Question 29

How is an Overflow calculated?

Answer 29

By XORing the top two carry bits from an addition/ subtraction.

Question 30

What does the Negative (N) flag represent?

Answer 30

It indicates whether the result of the last operation was negative (set to 1) or positive (set to 0) = copy of the sign bit.

Question 31

What is the Half-Carry (H) flag used for?

Answer 31

It indicates a carry or borrow from the lower 4 bits to the upper 4 bits during addition, especially useful in Binary Coded Decimal (BCD) operations.

Question 32

What does the Parity flag indicate? What is it useful for?

Answer 32

Parity describes whether the number of 1’s in a binary number is odd or even.
Useful for detecting or correcting errors in a communication system.

Question 33

What is the role of the Arithmetic Logic Unit (ALU)?

Answer 33

Performs operations on its inputs to create a single output value : two inputs, one destination. Status flags may be affected depending on the processor.

Question 34

What is the “Add with carry” operation in the ALU?

Answer 34

Adds two inputs along with the carry input, enabling multi-word operations and producing a new carry output.

Question 35

How is subtraction implemented in the ALU?

Answer 35

Achieved by taking the one’s or two’s complement of one input and feeding the inputs to the adder. A “Subtract with carry” operation accounts for the carry/borrow bit.

Question 36

What does the comparison operation do in the ALU?

Answer 36

Subtracts one input from the other (Source A - Source B).
Flags provide results like Zero (equal), Carry/Borrow, Negative, or Overflow.

Question 37

How does the negate operation work in the ALU?

Answer 37

It creates the two’s complement of a number by calculating { 0 - number } using the subtractor with one input set to zero.

Question 38

What logic operations are provided by the ALU?

Answer 38

Standard operations like AND, OR, NOT, XOR are performed bitwise. Additional instructions can test, set, or clear individual bits.

Question 39

What does a shift operation do in the ALU?

Answer 39

It moves all bits up or down the word. Left shifts multiply by 2, and right shifts divide by 2, often requiring sign extension.

Question 40

What differs Rotate from Shift in a ALU?

Answer 40

In rotation, bits moved off one end are placed in the vacant space at the other end.
Rotate through the carry bit is also possible in some cases.

Question 41

What is the result of multiplying two N-bit numbers in the ALU?

Answer 41

It produces a 2N-bit result. Low and high parts may be stored in separate registers. Special Multiply-and-Accumulate (MAC) instructions may be used for signal processing.

Question 42

What happens during division in the ALU?

Answer 42

Division produces a result and a remainder, often requiring two destinations. This operation is not always available.

Question 43

What is SIMD (Single Instruction, Multiple Data)?

Answer 43

It is a useful type of instruction for when the same operation is to be done on a large set of data points (e.g. increasing the brightness in an image).
They can speed up the performance of computers.