1. Comp Org & Assembly Lang
Bits and Bytes
Topics
Why bits?
Representing information as bits
Binary / Hexadecimal
Byte representations
Numbers
Characters and strings
Instructions
Bit-level manipulations
Boolean algebra
Expressing in C

2. Why Don’t Computers Use Base 10?
Base 10 Number Representation
That’s why fingers are known as “digits”
Natural representation for financial transactions
Floating point number cannot exactly represent $1.20
Even carries through in scientific notation
X (1.5213e4)

3. Why Don’t Computers Use Base 10?
Implementing Electronically
Hard to store
ENIAC (First electronic computer) used 10 vacuum tubes / digit
IBM 650 used 5+2 bits (1958, successor to IBM’s Personal Automatic Computer, PAC from 1956)
Hard to transmit
Need high precision to encode 10 signal levels on single wire
Messy to implement digital logic functions
Addition, multiplication, etc.

4. Binary Representations
Base 2 Number Representation
Represent as
Represent as [0011]…2
Represent X 104 as X 213
Electronic Implementation
Easy to store with bistable elements
Reliably transmitted on noisy and inaccurate wires
0.0V
0.5V
2.8V
3.3V 1

5. Encoding Byte Values Byte = 8 bits Binary 000000002 to 111111112
Decimal: to
First digit must not be 0 in C
Octal: to
Use leading 0 in C
Hexadecimal to FF16
Base 16 number representation
Use characters ‘0’ to ‘9’ and ‘A’ to ‘F’
Use leading 0x in C,
write FA1D37B16 as 0xFA1D37B
Or 0xfa1d37b
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111 8
1000 9
1001 A 10
1010 B 11
1011 C 12
1100 D 13
1101 E 14
1110 F 15
1111
Hex
Decimal
Binary

6. Bases Every number system uses a base Decimal numbers use base 10
Other common bases used in computer science:
Octal (base 8)
Hexadecimal (base 16)
Binary (base 2)
Do examples of base 10, base 8 numbers, base 16
Show how to translate base 8 to base 10, base 16 to base 10

7. Decimal
x x x 100

8. Octal
x x x 80

9. Counting in octal

10. Converting Converting octal to decimal:
753 = 7 x x x 80 = = 491

11. Translating to octal writing 157 in base 8
remainder:
2 x x x 80 = = 157
Divisor

12. Hexadecimal
x x x 160

13. Hexadecimal
A B C D E F
A 1B 1C 1D 1E 1F
A 2B 2C 2D 2E 2F
A 3B 3C 3D 3E 3F 40 41
A 4B 4C 4D 4E 4F 50
A 5B 5C 5D 5E 5F
A 6B 6C 6D 6E
6F A 7B 7C 7D
7E 7F A 8B 8C
8D 8E 8F
A 10B
10C 10D 10E 10F 120 …

14. Translating to hex 365 remainder: 16 22 D 1 6 0 1 1 6 D
1 6 D
1 x x D x 160 = = 365

15. Binary
x x x 20

16. Counting in binary

17. Translating to binary
4 remainder:
1 0
0 1
Divisor

18. Translating to binary
remainder:
2 1
1 0
0 1

19. Literary Hex Common 8-byte hex filler: 0xdeadbeef
Can you think of other 8-byte fillers?

20. Relation between hex and binary
Hexadecimal:
16 characters,
Each represents a number between 0 and 15
Binary:
Consider 4 places
Represent numbers between 0000 and 1111
Or between 0 and 15
Result:
1 hex digit represents 4 binary digits

21. Relation between hex and binary
Decimal
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111 8
1000 9
1001 10 A
1010 11 B
1011 12 C
1100 13 D
1101 14 E
1110 15 F
1111 16