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. Converting main() { octal_print(0); /* result: 00 */
octal_print( ); /* result: since 0 at */
/* beginning indicates octal num */
octal_print( ); /* result: */
octal_print(999); /* result: */
octal_print(-999); /* result: */
octal_print(1978); /* result: */ }

3. See /home/barr/Student/comp210/examples/octal.c
Converting
#define DIG 20
void octal_print(int x) {
int i = 0, od;
char s[DIG]; /* up to DIG octal digits */
if ( x < 0 ) /* treat negative x */
putchar ('-'); /* output a minus sign */
x = - x; } do
od = x % 8; /* next higher octal digit */
s[i++] = (od + '0'); /* octal digits in char form */
} while ( (x = x/8) > 0); /* quotient by integer division */
putchar('0'); /* octal number prefix */
putchar(s[--i]); /* output characters on s s*/
} while ( i > 0 );
putchar ('\n');
See /home/barr/Student/comp210/examples/octal.c

4. Memory Contents Address What is memory (RAM)?
To the processor, it’s just a big array of cells
Each cell has an address
Each cell contains a specific value
15213
“John”
Sunday
‘a’ 1 2 3 4
Address
Contents

5. Memory Contents Address
Of course, addresses and content are actually in binary
Memory is byte addressable i.e., every byte has an address.
Address 1
000
001
010
011
100
Contents

6. Memory Contents Address
When we look at memory in a debugger (like gdb), usually use hex notation
Address 9B 39 C3 5F 09
000
001
002
003
004
Contents

7. Memory What we see (gdb) x/20b 0x7fffffffe45c
0x7fffffffe45c: 0x5 0x0 0x0 0x0 0x1 0x0 0x0 0x0
0x7fffffffe464: 0x0 0x0 0x0 0x0 0xffffffffffffffdd 0x5 0x40 0x0
0x7fffffffe46c: 0x0 0x0 0x0 0x0

8. 32-bit machine means 32 wires on each bus
Addressing Memory
CPU must send an address to RAM how many bits in the address? depends on how many wires there are!
32-bit machine means 32 wires on each bus

9. Memory size limited by number of bits in address: 3 bits so 8 cells
Contents
000
001
010
011
100
101
110
111
How do we talk about the size of memory?
in terms of powers of 2 (addresses are binary)
Bus must have 3 wires
Memory size limited by number of bits in address: 3 bits so 8 cells

10. Range
An address has a fixed number of bits.
The range is the numbers that will fit in that many bits.
Examples:
= 0
= 7 range is 0 to 7
= 0
= 15 range is 0 to 15

11. Range
In general range is 0 to 2n – 1 where there are n bits in the representation
Intuition:
111 = 1 x x x 20
Which is 1 less than
1000 = 1 x x x x 20
Number of numbers represented:
n bits can represent 2n different numbers
i.e., from 0 to 2n – 1

12. Size
In general Size is 2n where there are n bits in the representation
Intuition:
Range of 3 bits: = 0
= 7 range is 0 to 7
number of numbers is 8 = 23 or 1 more than the largest number!
Number of numbers represented:
n bits can represent 2n different numbers
i.e., from 0 to 2n – 1

13. Memory How do we talk about the size of memory?
in terms of powers of 2 (addresses are binary) based on the number of bits in the address 20 1 21 2 22 4 23 8 24 16 25 32 26 64 27
128 28
256 29
512
210
1024
211
2048
212
4096
213
8192
214
16384
210 x 210 = 220
1,048,576
210 x 210 x 210 = 230
1,073,741,824
210 x 210 x 210 x 210 = 240
1,099,511,627,776

14. Memory How do we talk about the size of memory? 1 bit 8 bits 1 byte
in bytes (how may bytes of memory do you have?)
in terms of powers of 2 (addresses are binary)
1 bit
8 bits
1 byte
210 bytes
1024 bytes
210 x 210 = 220
1,048,576 bytes
210 x 210 x 210 = 230
1,073,741,824 bytes
210 x 210 x 210 x 210 = 240
1,099,511,627,776 bytes
1 bit
1 byte
1 Kilobyte (Kb)
1 Megabyte (Mb)
1 Gigabyte (Gb)
1 Terabyte (Tb)