This is a way of representing numbers i.e your fingers

This is when a numbers position defines its weight, for example in our number system moving to the left increase the weight by 10

place-value notation

base 10

0 to 9

$10^n$

sum(weight(is it in the tens or hundreds) * digit(is its a 9 or 1))

The base value of a number

base 2

0 to 1

base 8

0 to 7

A positive and Negative number respectively

1. Subtract the largest 2^n you can

2. Add a one

3. 2^(n-1) if cannot subtract then add a 0 else add a 1

4. repeat until you reach 2^0

1 or 0

4 bits

8 bits or 2 nibbles

The amount of data the cpu can process in one go, i.e. 32bit or 64bit

This is where the largest bit represents 1 = -ve and 0 = +ve

1. Add like normal, so if
   1. 1 + 1 = carry the one
   2. 0 + 1 = 1
   3. 0 + 0 = 0

2. If you get a overflow carry it around to the start and add it

1. Flip all bits

It is both, thats why it is bad

Carry it to the start and add it

1. If the signed bit is negative (1), filp all bits

2. Add the bits up

This is where the most significant bit is negative

• It is slow

• It is hard to implement into hardware

• Doesn't have the -+0 problem

Leave it, on the left

SB +-

1s -7 (flip everything then read it)

2s -8

Flip all bits and then add one

1. Look at the bottom row, look at the first bit, multiply that by each bit above

2. Once completed shift to the left, then repeat till no more bits

3. Finally add them

0000 0101

0000 0011

0000 0101

0000 1010 +

0000 1111

base 16

1. 1

2. 2

3. 3

4. 4

5. 5

6. 6

7. 7

8. 8

9. 9

10. A

11. B

12. C

13. D

14. E

15. F

first split into groups of nibbles

0100 1101

then convert the nibbles into denery

4 D