1. Binary & Decimal numbers

2. Decimal system: Ten digits: 0,1,2,3,…,9 3185
Example:
= 3* * *10 + 5*1
= 3* * * *100

3. 10110 Binary system: Two digits: 0,1
Example:
1*(24) + 0*(23) + 1*(22) + 1*(21) + 0*(20)

4. Byte and Bit 1 Bit: (binary digit) either 0 or 1
Byte: an ordered collection of 8 bits 1
MSB
(Most significant bit)
LSB
(Least significant bit)

5. Binary to Decimal 1 23 + 21 + 20 = 11 * 27 26 25 24 23 22 21 20 0*(27)1 * 27 26 25 24 23 22 21 20
0*(27)
0*(26)
0*(25)
0*(24)
1*(23)
0*(22)
1*(21)
1*(20)
= 11

6. Decimal to Binary 25 1 [25%2=1] 12 [25/2=12] 0 [12%2=0] 6 [12/2=6]
0 [6%2=0]
3 [6/2=2]
1 [3%2=1]
1 [3/2=1]
1 [1%2=1]
0 [1/2=0]
Right 1 2 3 4 5 6 7 8 9
Left 10
25 (decimal) = (binary)

7. Overflow 1 1 The highest number represented by 8 bits is 255 (why?).
What happens when we add 1 to it? 1
The bit is lost !