The document discusses various components of computer arithmetic units including half adders, full adders, ripple carry adders, and carry look ahead adders. It also covers binary addition algorithms like Booth's algorithm. Memory types like RAM and ROM are compared, with RAM being volatile and allowing both read and write access while ROM is non-volatile and only allows read access. Truth tables and circuit diagrams are provided for half adders, full adders, and adders used in binary addition.

1. Computer Architecture and
Microprocessors
Unit 2:Arithmatic Unit
Amruta R. Chougale

2. • Decimal to binary conversion.
• One’s and Two’s Complement.
• Logical gates.
• Signed and Unsigned No.s
• Addition and subtraction of signed nos
• Half Adder
• Kmap
• Full Adder

3. Flow chart for Signed no

4. Half Adder
• A half adder is a type of adder, an electronic
circuit that performs the addition of numbers.
• The half adder is able to add two single binary
digits and provide the output plus a carry
value.
• It has two inputs, called A and B, and two
outputs S (sum) and C (carry).

5. Truth Table
A (input) B (input) C (output) S (output)
0 0 0 0
1 0 0 1
0 1 0 1
1 1 1 0
Half Adder truth table:

6. Kmap generation
used to facilitate the simplification of Boolean
algebra functions.

7. Full Adder
• Full Adder is the adder which adds three inputs
and produces two outputs.
• The first two inputs are A and B and the third
input is an input carry as C-IN.
• The output carry is designated as C-OUT and the
normal output is designated as S which is SUM.
• A full adder logic is designed in such a manner
that can take eight inputs together to create a
byte-wide adder and cascade the carry bit from
one adder to the another.

8. Block Diagram for Full Adder

9. Truth Table

10. • Logical Expression for SUM:
= A’ B’ C-IN + A’ B C-IN’ + A B’ C-IN’ + A B C-IN
= C-IN (A’ B’ + A B) + C-IN’ (A’ B + A B’)
= C-IN XOR (A XOR B)
= (1,2,4,7)
• Logical Expression for C-OUT:
= A’ B C-IN + A B’ C-IN + A B C-IN’ + A B C-IN
= A B + B C-IN + A C-IN
= (3,5,6,7)

11. Full Adder circuit diagram

12. Ripple carry adder/ 4 Bit binary adder
• In Digital Circuits, A Binary Adder-
Subtractor is one which is capable of both
addition and subtraction of binary numbers in
one circuit itself.
• The operation being performed depends upon
the binary value the control signal holds. It is
one of the components of the ALU (Arithmetic
Logic Unit).

13. Circuit diagram 4 bit adder

14. Carry look ahead adder

15. Truth table

16. Circuit diagram

17. BOOTHS Algo.

18. Modified booths algo

19. Memory
RAM & ROM

20. Difference between
Basis for Comparison RAM ROM
Stands for Random Access Memory Read Only Memory
Memory type Volatile Non-volatile
Memory capacity 1 to 256 GB per chip 4 to 8 MB per chip
Operation type Read and Write both. Only Read.
Speed Fast Comparatively slow.
Storage type Temporary Permanent
Also referred as Primary memory Secondary memory
Presence of data according to power
source
The stored data in RAM lost in case
of power failure.
Data retained in ROM even if the
power is turned off.
Accessibility to processor Processor can directly access the
data in RAM.
Processor cannot directly access
the data in ROM.
Cost High Comparitively low
Types SRAM and DRAM PROM, EPROM and EEPROM