1. Cs 121 Ch 4-2 Combinational Logic
Give qualifications of instructors:
DAP
teaching computer architecture at Berkeley since 1977
Co-athor of textbook used in class
Best known for being one of pioneers of RISC
currently author of article on future of microprocessors in SciAm Sept 1995 RY
took 152 as student, TAed 152,instructor in 152
undergrad and grad work at Berkeley
joined NextGen to design fact 80x86 microprocessors
one of architects of UltraSPARC fastest SPARC mper shipping this Fall

2. Subtractors Half Subtractor Full Subtractor credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

3. QUIZ
Subtract binary number 11 from 1010 01 10 1 1 1 1 1

4. 1 2 -1 1 Half Subtractor Subtract two binary numbers 0 0 0 0 0 1 1 1
Half-Subtractor (HS), a 2-input bit-wise Subtractor functional block.
Subtract two binary numbers
A0 , B0 -> single bit inputs
D0 -> single bit difference
Bo -> Borrow out A B D B
Block diagram o A B D o
(difference) 1 2
(borrow out) -1 1
Circuit diagram

5. Logic Simplification: Half Subtractor
The K-Map for Do, Bo is: B A 1 3 2 Do Bo B A Do Å = × + A B A Bo × = A B D o
(difference)
(borrow out)

6. QUIZ ? Q#1- What is the difference and borrow outputs from
This half-subtractor circuit?
Q#2- What is the difference and borrow outputs from
this half-subtractor circuit?
Q#3- What is the difference and borrow outputs from
this half-subtractor circuit?
Q#4- What is the difference and borrow outputs from
this half-subtractor circuit?
ANS: Di= 0, Bo= 0
ANS: Di= 1, Bo= 0
ANS: Di= 0, Bo= 0
ANS: Di= 1, Bo= 1
(A – B)
A = 0
B = 0
(A – B)
A = 1
B = 0
(A – B)
A = 1
B = 1
(A – B)
A = 0
B = 1 ?

7. Di Same as Si in full adder Full Subtractor Bin Ai Bi Di Bo Bin AiBi
Full-Subtractor (FS), a 3-input bit-wise Subtractor functional block
Bin Ai Bi Di Bo
Bin
AiBi 00 01 11 10 1 1 1 1 1 Di
We going to use Ci as Bin
Ci+1 as Bo
Di = Ci Å (Ai Å Bi)
Same as Si in full adder
Note: 3 inputs

8. Ci+1 Full Subtractor Ci AiBi 00 01 11 10 1 Ci Ai Bi Di Ci+1 0 0 0 0 0
Now consider implementation of Borrow out Ci+1
Remember Two outputs per full Subtractor bit (Ci+1, Si) Ci
AiBi 00 01 11 10 1
Ci Ai Bi Di Ci+1 1 1 1 1
Ci+1
Ci+1 = !Ai Bi
+ !Ai !Bi
+ Ci Ai Bi
Note: 3 inputs
Note: 2 out- puts

9. Recall: Full Subtractor Ci+1 = !Ai Bi +Ci !Ai !Bi +Ci Ai Bi
+ Ci(!Ai !Bi + Ai Bi)
Ci+1 = !Ai Bi + Ci !(Ai Å Bi)
Recall:
Di = Ci Å (Ai Å Bi)
Ci+1 = !Ai Bi +Ci !(Ai Å Bi)

10. half subtractor Full Subtractor Di = Ci Å (Ai Å Bi)
Ci+1 = !Ai Bi + Ci !(Ai Å Bi)
half subtractor

11. QUIZ ? Q#1- What are the Difference and Borrow out output from
this full-subtractor circuit?
Q#2- What are the Difference and Borrow out output from
this full-subtractor circuit?
Q#3- What are the Difference and Borrow out output from
this full-subtractor circuit?
Q#4- What are the Difference and Borrow out output from
this full-subtractor circuit?
Q#5- What are the Difference and Borrow out output from
this full-subtractor circuit?
Q#6- What are the Difference and Borrow out output from
this full-subtractor circuit?
ANSWER: Di = 0, Bo = 0
ANSWER: Di = 1, Bo = 1
ANSWER: Di = 1, Bo = 1
ANSWER: Di = 0, Bo = 1
ANSWER: Di = 1, Bo = 0
ANSWER: Di = 0, Bo = 0
(A – B - Bin)
Bin = 0
A = 0
B = 0
(A – B - Bin)
Bin = 1
A = 0
B = 0 ?
(A – B - Bin)
Bin = 1
A = 1
B = 1
(A – B - Bin)
Bin = 1
A = 0
B = 1
(A – B - Bin)
Bin = 0
A = 1
B = 0
(A – B - Bin)
Bin = 0
A = 1
B = 1