Basic arithmetic, instruction execution and program

Machine Instructions and
Programs

Number, Arithmetic Operations,
and Characters

Signed Integer
• 3 major representations:
Sign-magnitude
One’s complement
Two’s complement
• Assumptions:
4-bit machine word
16 different values can be represented
Roughly half are positive, half are negative

Sign and Magnitude Representation
0000
0111
0011
1011
1111
1110
1101
1100
1010
1001
1000
0110
0101
0100
0010
0001
+0
+1
+2
+3
+4
+5
+6
+7
-0
-1
-2
-3
-4
-5
-6
-7
0 100 = + 4
1 100 = - 4
+
-
High order bit is sign: 0 = positive (or zero), 1 = negative
Three low order bits is the magnitude: 0 (000) thru 7 (111)
Number range for n bits = +/-2n-1 -1
Two representations for 0

One’s Complement Representation
• Subtraction implemented by addition & 1's complement
• Still two representations of 0! This causes some problems
• Some complexities in addition
0000
0111
0011
1011
1111
1110
1101
1100
1010
1001
1000
0110
0101
0100
0010
0001
+0
+1
+2
+3
+4
+5
+6
+7
-7
-6
-5
-4
-3
-2
-1
-0
0 100 = + 4
1 011 = - 4
+
-

Two’s Complement Representation
• Only one representation for 0
• One more negative number than positive number
0000
0111
0011
1011
1111
1110
1101
1100
1010
1001
1000
0110
0101
0100
0010
0001
+0
+1
+2
+3
+4
+5
+6
+7
-8
-7
-6
-5
-4
-3
-2
-1
0 100 = + 4
1 100 = - 4
+
-
like 1's comp
except shifted
one position
clockwise

Binary, Signed-Integer Representations
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
+
1
-
2
+
3
+
4
+
5
+
6
+
7
+
2
-
3
-
4
-
5
-
6
-
7
-
8
-
0
+
0
-
1
+
2
+
3
+
4
+
5
+
6
+
7
+
0
+
7
-
6
-
5
-
4
-
3
-
2
-
1
-
0
-
1
+
2
+
3
+
4
+
5
+
6
+
7
+
0
+
7
-
6
-
5
-
4
-
3
-
2
-
1
-
b3 b2b1b0
Sign and
magnitude 1's complement 2's complement
B Values represented
Binary, signed-integer representations.

Addition and Subtraction – 2’s Complement
4
+ 3
7
0100
0011
0111
-4
+ (-3)
-7
1100
1101
11001
4
- 3
1
0100
1101
10001
-4
+ 3
-1
1100
0011
1111
If carry-in to the high
order bit =
carry-out then ignore
carry
if carry-in differs from
carry-out then overflow
Simpler addition scheme makes twos complement the most common
choice for integer number systems within digital systems

2’s-Complement Add and Subtract
Operations
1 1 0 1
0 1 1 1
0 1 0 0
0 0 1 0
1 1 0 0
1 1 1 0
0 1 1 0
1 1 0 1
0 0 1 1
1 0 0 1
0 1 0 1
1 1 1 0
1 0 0 1
1 1 1 1
1 0 0 0
0 0 1 0
0 0 1 1
0 1 0 1
4
+
( )
2
-
( )
3
+
( )
2
-
( )
8
-
( )
5
+
( )
+
+
+
+
+
+
1 1 1 0
0 1 0 0
1 0 1 0
0 1 1 1
1 1 0 1
0 1 0 0
6
-
( )
2
-
( )
4
+
( )
3
-
( )
4
+
( )
7
+
( )
+
+
(b)
(d)
1 0 1 1
1 1 1 0
1 0 0 1
1 1 0 1
1 0 0 1
0 0 1 0
0 1 0 0
0 1 1 0
0 0 1 1
1 0 0 1
1 0 1 1
1 0 0 1
0 0 0 1
0 0 1 0
1 1 0 1
0 1 0 1
0 0 1 0
0 0 1 1
5
-
( )
2
+
( )
3
+
( )
5
+
( )
2
+
( )
4
+
( )
2
-
( )
7
-
( )
3
-
( )
7
-
( )
6
+
( )
3
+
( )
1
+
( )
7
-
( )
5
-
( )
7
-
( )
2
+
( )
3
-
( )
+
+
-
-
-
-
-
-
(a)
(c)
(e)
(f)
(g)
(h)
(i)
(j)
2's-complement Add and Subtract operations.

Overflow - Add two positive numbers to get a negative
number or two negative numbers to get a positive number
5 + 3 = -8 -7 - 2 = +7
0000
0001
0010
0011
1000
0101
0110
0100
1001
1010
1011
1100
1101
0111
1110
1111
+0
+1
+2
+3
+4
+5
+6
+7
-8
-7
-6
-5
-4
-3
-2
-1
0000
0001
0010
0011
1000
0101
0110
0100
1001
1010
1011
1100
1101
0111
1110
1111
+0
+1
+2
+3
+4
+5
+6
+7
-8
-7
-6
-5
-4
-3
-2
-1

Overflow Conditions
5
3
-8
0 1 1 1
0 1 0 1
0 0 1 1
1 0 0 0
-7
-2
7
1 0 0 0
1 0 0 1
1 1 0 0
1 0 1 1 1
5
2
7
0 0 0 0
0 1 0 1
0 0 1 0
0 1 1 1
-3
-5
-8
1 1 1 1
1 1 0 1
1 0 1 1
1 1 0 0 0
Overflow Overflow
No overflow No overflow
Overflow when carry-in to the high-order bit does not equal carry out

Sign Extension
• Task:
– Given w-bit signed integer x
– Convert it to w+k-bit integer with same value
• Rule:
– Make k copies of sign bit:
– X ′ = xw–1 ,…, xw–1 , xw–1 , xw–2 ,…, x0
k copies of MSB
• • •
X
X ′ • • • • • •
• • •
w
w
k

Sign Extension Example
short int x = 15213;
int ix = (int) x;
short int y = -15213;
int iy = (int) y;
Decimal Hex Binary
x 15213 3B 6D 00111011 01101101
ix 15213 00 00 C4 92 00000000 00000000 00111011 01101101
y -15213 C4 93 11000100 10010011
iy -15213 FF FF C4 93 11111111 11111111 11000100 10010011

Memory Locations, Addresses,
and Operations

Memory Location, Addresses, and
Operation
• Memory consists of
many millions of
storage cells, each
of which can store 1
bit.
• Data is usually
accessed in n-bit
groups. n is called
word length.
second word
first word
Memory words.
nbits
last word
i th word
•
•
•
•
•
•

Operation
• 32-bit word length example
(b) Four characters
character
character
character character
(a) A signed integer
Sign bit: for positive numbers
for negative numbers
ASCII
ASCII
ASCII
ASCII
32 bits
8 bits 8 bits 8 bits 8 bits
b31 b30 b1 b0
b31 0
=
b31 1
=
•
•
•

Operation
• To retrieve information from memory, either for one
word or one byte (8-bit), addresses for each location are
needed.
• A k-bit address memory has 2k memory locations, namely
0 – 2k-1, called memory space/ address space.
• 24-bit memory: 224 = 16,777,216 = 16M (1M=220)
• 32-bit memory: 232 = 4G (1G=230)
• 1K(kilo)=210
• 1T(tera)=240

Operation
• It is impractical to assign distinct addresses to
individual bit locations in the memory.
• The most practical assignment is to have
successive addresses refer to successive byte
locations in the memory – byte-addressable
memory.
• Byte locations have addresses 0, 1, 2, … If
word length is 32 bits, they successive words
are located at addresses 0, 4, 8,…

Big-Endian and Little-Endian
Assignments
2
k
4
- 2
k
3
- 2
k
2
- 2
k
1
- 2
k
4
-
2
k
4
-
0 1 2 3
4 5 6 7
0
0
4
2
k
1
- 2
k
2
- 2
k
3
- 2
k
4
-
3 2 1 0
7 6 5 4
Byte address
Byte address
(a) Big-endian assignment (b) Little-endian assignment
4
Word
address
•
•
•
•
•
•
Figure 2.7. Byte and word addressing.
Big-Endian: lower byte addresses are used for the most significant bytes of the word
Little-Endian: opposite ordering. lower byte addresses are used for the less significant
bytes of the word

Operation
• Address ordering of bytes
• Word alignment
– Words are said to be aligned in memory if they
begin at a byte addr. that is a multiple of the num
of bytes in a word.
• 16-bit word: word addresses: 0, 2, 4,….
• 32-bit word: word addresses: 0, 4, 8,….
• 64-bit word: word addresses: 0, 8,16,….
• Access numbers, characters, and character
strings

Memory Operation
• Load (or Read or Fetch)
 Copy the content. The memory content doesn’t change.
 Address – Load
 Registers can be used
• Store (or Write)
 Overwrite the content in memory
 Address and Data – Store
 Registers can be used

Instruction and Instruction
Sequencing

“Must-Perform” Operations
• Data transfers between the memory and the
processor registers
• Arithmetic and logic operations on data
• Program sequencing and control
• I/O transfers

Register Transfer Notation
• Identify a location by a symbolic name
standing for its hardware binary address (LOC,
R0,…)
• Contents of a location are denoted by placing
square brackets around the name of the
location (R1←[LOC], R3 ←[R1]+[R2])
• Register Transfer Notation (RTN)

Assembly Language Notation
• Represent machine instructions and programs.
• Move LOC, R1 = R1←[LOC]
• Add R1, R2, R3 = R3 ←[R1]+[R2]

CPU Organization
• Single Accumulator
– Result usually goes to the Accumulator
– Accumulator has to be saved to memory quite often
• General Register
– Registers hold operands thus reduce memory traffic
– Register bookkeeping
• Stack
– Operands and result are always in the stack

Instruction Formats
• Three-Address Instructions
– ADD R1, R2, R3 R3 ← [R1] + [R2]
• Two-Address Instructions
– ADD R1, R2 R2 ← [R1] + [R2]
• One-Address Instructions
– ADD M AC ← AC + [M]
• Zero-Address Instructions
– ADD TOS ← [TOS] + [(TOS – 1)]
• RISC Instructions
– Lots of registers. Memory is restricted to Load & Store
Opcode Operand(s) or Address(es)

Instruction Formats
Example: Evaluate X = (A+B) ∗ (C+D)
• Three-Address
1. ADD A, B, R1 ; R1 ← [A] + [B]
2. ADD C, D, R2 ; R2 ← [C] + [D]
3. MUL R1, R2, X ; X ← [R1] ∗ [R2]

Instruction Formats
• Two-Address
1. MOV A, R1 ; R1 ← [A]
2. ADD B, R1 ; R1 ← [R1] + [B]
3. MOV C, R2 ; R2 ← [C]
4. ADD D, R2 ; R2 ← [R2] + [D]
5. MUL R2, R1 ; R1 ← [R1] ∗ [R2]
6. MOV R1, X ; X ← [R1]

Instruction Formats
• One-Address
1. LOAD A ; AC ← [A]
2. ADD B ; AC ← [AC] + [B]
3. STORE T ; T ← [AC]
4. LOAD C ; AC ← [C]
5. ADD D ; AC ← [AC] + [D]
6. MUL T ; AC ← [AC] ∗ [T]
7. STORE X ; X ← [AC]

Instruction Formats
• Zero-Address
1. PUSH A ; TOS ← [A]
2. PUSH B ; TOS ← [B]
3. ADD ; TOS ← [A] + [B]
4. PUSH C ; TOS ← [C]
5. PUSH D ; TOS ← [D]
6. ADD ; TOS ← [C] + [D]
7. MUL ; TOS ← (C+D)∗(A+B)
8. POP X ; X ← [TOS]

Instruction Formats
• RISC
1. LOAD A, R1 ; R1 ← [A]
2. LOAD B, R2 ; R2 ← [B]
3. LOAD C, R3 ; R3 ← [C]
4. LOAD D, R4 ; R4 ← [D]
5. ADD R1, R2, R1 ; R1 ← [R1] + [R2]
6. ADD R3, R4, R3 ; R3 ← [R3] + [R4]
7. MUL R1, R3, R1 ; R1 ← [R1] ∗ [R3]
8. STORE R1, X ; X ← [R1]

Using Registers
• Registers are faster
• Shorter instructions
– The number of registers is smaller (e.g. 32
registers need 5 bits)
• Potential speedup
• Minimize the frequency with which data is
moved back and forth between the memory
and processor registers.

Basic arithmetic, instruction execution and program

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