Binary & Int representations | Bitwise Operations

Question 1

voltage for binary numbers

Answer 1

0: 0V
1: 3.3V

Question 2

How many bit patters can an n-bit register hold?

Answer 2

2^n bit patters

Question 3

Range of unsigned integers and how are they encoded?

Answer 3

Range: 0 to (2^n)-1
Encoded using binary numbers

Question 4

Range of signed integers and how are they encoded?

Answer 4

Range: -(2^n-1) to (2^n-1)-1
Encoded using two’s complement

Question 5

How is a number negated?

Answer 5

1. Take one’s complement (flip bits)
2. Add 1 to the result

Question 6

How to distinguish a +/- signed int?

Answer 6

The leftmost bit is the signed bit. 0 = + and 1 = -

Question 7

Do we use sign-magnitude and one’s complement of signed integers?

Answer 7

No, they are awkward to handle in hardware, they have +0 and -0. Rarely used today.

Question 8

What are hex numbers commonly used for?

Answer 8

Shorthands for denoting bit patterns

Question 9

What data model does Linux on ARMv8 in AArch 64 use?

Answer 9

LP64 data model
Long ints and
Pointers are
64 bits long

Question 10

What are the 5 A64 keywords, their sizes in bits and corresponding C keyword?

Answer 10

1. Byte, 8 bits, char
2. Halfword, 16 bits, short int
3. Word, 32 bits, int
4. Doubleword, 64 bits, long int / void
5. Quadword, 128, N/A

Question 11

How to define an unsigned integer in C?

Answer 11

unsigned int x;
or for char
unsigned char x;

Question 12

What do bitwise logical instructions do?

Answer 12

Manipulate 1 or more bits in a register

Question 13

what’s it called when these two are anded together and the result is all 0’s
1010
0000
———
0000

Answer 13

A bitmask “masks out” these bits

Question 14

Check if bit 3 is set in x20

Answer 14

uses ands, check notes

Question 15

set bits 4&5 in x20

Answer 15

uses orr, check notes
orr doesn’t need an s

Question 16

What does bit clear mean and what is its opcode?

Answer 16

AND NOT, bic

Question 17

Clear bits 2-5 in x20

Answer 17

use bic (bitclear), check notes

Question 18

Opcode for exclusive or

Answer 18

eor

Question 19

Opcode for OR NOT

Answer 19

orn

Question 20

NOT opcode and what is it an alias for?

Answer 20

mvn xd, xm
(move not)
Alias for: orn xd, xzr, xm

Question 21

Exclusive or not opcode

Answer 21

eon

Question 22

Explain rotate right and what is its opcode?

Answer 22

Bits shifted out the right are inserted on the left.
ror

Question 23

Explain Signed Extend Byte and what is its opcode?

Answer 23

Sign-extends bit 7 to bits 8-31
stxb

Question 24

What are all the sign-extend operations, what do they do and what registers do they use?

Answer 24

1. Signed Extend Byte: extends bits 8-31, uses w
2. Signed Extend Halfword: extends bits 15 to bits 16-31, uses w
3. Signed Extend Word: extends bits 31 to bits 32-64, uses x

Question 25

What are the unsigned extend operations?

Answer 25

1. Unsigned extend byte: uxtb, take something that’s 8 bits wide, extend it to 32
2. Unsigned extend halfword: uxth, takes something that’s 16 bits wide and extend to 32
3. Unsigned extend word: uxtw, takes something that’s 32 bits wide, extends it to 64

Question 26

What does modulus arithmetic do?

Answer 26

• Constrains numbers to the range 0 to M-1 where M is the modulus. - CPUs normally do modulus arithmetic.
• If n is the size in bits, M=2^n
• Carry out is ignored

Question 27

On a 4-bit CPU, what does 9+8 give?

Answer 27

(9+8) mod 16 = 1

Question 28

What can adds or subs be used for and what new flag gets set compared to ands?

Answer 28

Can be used for extended precision arithmetic and carry flag is set.

Question 29

Full adder circuit diagram

Answer 29

Check notes

Question 30

How are multi-bit numbers summed in hardware?

Answer 30

Using multiple full adder circuits (1 for each bit). See diagram in notes

Question 31

How is subtraction done in the ALU?

Answer 31

Negating the subtrahend and then adding. In 7-5, 5 is the subtrahend. The carry out is also ignored here.

Question 32

Subtract 7-5 in binary

Answer 32

2 but check notes on how it’s done

Question 33

What flags for signed branch instructions use?

Answer 33

N,Z,V

Question 34

How does the V flag work for subtraction? Also how to subtract -8 - 5?

Answer 34

V=true if xd=0, xn=1, xm=1 or xd=1, xn=0, xm=0
For -8-5, negate both binary representations of 8 and 5. Add.

Question 35

Difference between unsigned and signed arithmetic

Answer 35

Both use the same registers and hardware, but in unsigned, one interprets the data as unsigned numbers. A carry out indicates an overflow

Question 36

Chart for unsigned branching conditions

Answer 36

We use C instead of V
- eq, equal, ==, Z=1
- ne, not equal, !=, Z=0
- hi, higher than, >, Z==0 && C==1
- hs, higher than or same, >=, C==1
- lo, lower than, <, C==0
- ls, lower than or same, <=, !(Z==0 && C==1)

Question 37

What does an if statement use for branching conditions?

Answer 37

Logical complement

Question 38

How is binary multiplication done?

Answer 38

• Repeated for every bit in the source register, each step consists of 2 sub-steps:
  1. a conditional addition
  2. an asr
• If the original multiplier is negative, an extra step is needed: subtract the multiplicand from the high-order part of the result (from the product register)

Question 39

Where is the product of binary multiplication put?

Answer 39

In 2 concatenated registers