Binary Arithmetic

Question 1

What is the range for Modulus Arithmetic?

Answer 1

0 to M-1 Where M is the modulus

Question 2

Calculation results must fit into a fixed-size register If n is the size in bits, then M = __?

Answer 2

M = 2^n E.g. M is 16 for a 4-bit register

Question 3

Unsigned integers range from _ to _

Answer 3

0 to 15 (0000 to 1111)

Question 4

9 + 8 with arithmetic instructions

Answer 4

Question 5

Which flag do adds and subs set?

What can it be used for?

Answer 5

The Carry flag

Can be used to do extended precision arithmetic

Question 6

Rules for adding single bits

Answer 6

Question 7

What are the rules implemented by a full adder circuit?

Answer 7

Question 8

How is subtraction carried out?
Which part of the CPU does the subtracting?

Answer 8

It is done in the ALU by negating the subtrahend (what is subtracted) and adding it

It reuses the addition circuitry, thus minimizing hardware complexity

Question 9

Which flags do the signed branch instructions use?

Answer 9

N, Z, V flags

N = (Xd<63> == 1)

Z = (Xd == 0)

V = ((Xn<63> & -Xm<63> & -Xd<63>) | (-Xn<63> & Xm<63> & Xd<63>))

Question 10

Which instruction sets the flags using these rules?

Answer 10

subs (alias of cmp)

Question 11

When does overflow occur?

Answer 11

When the sign bits for Xn, Xm, and Xd are:

1,0,0
or
0,1,1

Question 12

Signed Number Branching Conditions example

Answer 12

Question 13

What does one interpret the data as in unsigned arithmetic?

Answer 13

unsigned integers

Question 14

When adding, which flag indicates overflow?

Answer 14

a carry out (C= 1)

Question 15

Unsigned Number Branching Conditions Table

Answer 15

Must use these condition codes in conditional branches when comparing integers

Question 16

What are the two sub-steps in a step for multiplication?

Answer 16

A conditional addition

An arithmetic shift right

Question 17

How many bits does the product require? And why?

Answer 17

Twice as many as those for source registers because the result is put into 2 concatenated registers

Question 18

If the original multiplier is negative, which step is needed?

Answer 18

Subtract the multiplicand from the high-order part of the result (i.e. from the product register)

Question 19

4-bit example of multiplication

Answer 19

Question 20

How is division carried out?

Answer 20

Can be done using an iterated procedure similar to manual long division

Question 21

When is extended precision arithmetic used?

How is it archived?

Answer 21

Is used when you need more than 64 bits of precision

Archived using 2 or more registers to represent a number e.g. 192-bit unit uses 3 registers x19 x20 x21

Question 22

What is the procedure to adding extended precision numbers together?

Answer 22

Question 23

Which instructions use the C flag when adding?

Answer 23

The adc and adcs instructions