Alu Design

Arithmetic Circuits

Goal for Today

Arithmetic
COMP375 Computer Architecture and O d Organization i ti

• Create logic gates that perform arithmetic

Elementary School
17 [phone] +000111 011000

1 Bit Adder
• A one bit adder has three inputs, numbers A and B and Carry in. There are two outputs, the Sum and Carry out. t t th S dC t
A B

You add two numbers together. If the sum is greater than the number base, you add one to the next column. When you add two numbers, you may also have to add the carry from the column to the right.

Cout

one bit adder

Cin

Sum

COMP375

1

Arithmetic Circuits

Multiple Bit Adder

1 bit Adder Truth Table

A

B

A

B

A

B

Cout

one bit adder

one bit adder

one bit adder

Sum

Sum

Sum figure from textbook

Addition Sum
A’ B’ Cin’ Cin 0 1 A’ B 1 0 A B 0 1 A B’ 1 0 Cin’ Cin

Addition Carry Out
A’ B’ 0 0 A’ B 0 1 A B 1 1 A B’ 0 1

Sum = A’BC’ + AB’C’ + A’B’C + ABC

Cout = AB + BC + AC

COMP375

2

Arithmetic Circuits

One bit adder
01000 + 01001 10001
(8) (9)

Overflow
• If operands are too big, then sum cannot be represented as an n-bit 2’s complement number. carry into sign bit carry out of sign bit

(-15)

11000 + 10111 01111

(-8) (-9) (+15)

• We have overflow if:
– signs of both operands are the same and same, – sign of sum is different.

• Another test -- easy for hardware:
– carry into left most bit does not equal carry out

Detecting Overflow

Intel Status Register

• When the carry into the sign bit does not match the carry out, there is an overflow

COMP375

3

Arithmetic Circuits

Saving Status
Status flag Overflow Sign Zero Carry Detection XOR of carry into and out of the sign bit Copy of the sign bit NOR of all result bits Carry into the sign bit

Intel Status Register
• The status register records the results of executing the instruction. ti th i t ti • Performing arithmetic sets the status register. • The compare instruction does a subtraction, subtraction but doesn t store the results. doesn’t results It just