Binary Mathematics

(101 * 10 = 1010) <- Shifts 1 Column

(101 * 11 = 101 + 1010 = 1111) <- Do individually and then add [11 = 10 + 1]

2= 0010

1= 0001

0 = 0000

-1= 1111 [Also 15]

-2 = 1110 [Also 14]

etc.

1000 [Highlighted is the most significant bit which is reserved for the sign (IF SIGNED)

How to work out a negative number in binary

1) work out the positive equivilent (e.g. 01100 = 12)

2) Copy from right until first one (e.g. 100)

3) Invert the rest (e.g. 10100 = -12)

[...000]01100

[...111]10100

These numbers carry on forever to the left with the same digit as they are signed

• The rules for negatives with binary point remain the same

e.g.

8  4  2  1  .  1/2  1/4  1/8

0  0  1  1  .   1     0     0

• The values after the binary point add up the same as the whole numbers