CSCI 162 Midterm Reference Sheet

Boolean logic identities

Inversion:      0' = 1
                1' = 0

Involution:     X'' = X

Dominance:      X+1 = 1
                X*0 = 0

Identity:       X+0 = X
                X*1 = X

Idempotence:    X+X = X
                X*X = X

Compliment:     X+X' = 1
                X*X' = 0

Commutativity:  X+Y = Y+X
                X*Y = Y*X

Associativity:  X+(Y+Z) = (X+Y)+Z
                X*(Y*Z) = (X*Y)*Z

Distributivity: X+(Y*Z) = (X+Y)*(X+Z)
                X*(Y+Z) = (X*Y)+(X*Z)

Absorption:     X*(X+Y) = X
                X+(X*Y) = X

DeMorgans:      X+Y = (X'*Y')'
                X*Y = (X'+Y')'

Powers of 2

  hex decimal octal
20 1 1 1
21 2 2 2
22 4 4 4
23 8 8 10
24 10 16 20
25 20 32 40
26 40 64 100
27 80 128 200
28 100 256 400
29 200 512 1000
210 400 1024 2000
211 800 2048 4000
212 1000 4096 10000
213 2000 8192 20000
214 4000 16384 40000
215 8000 32768 100000
216 10000 65536 200000

Hex:
A=10, B=11, C=12,
D=13, E=14, F=15

Marie instructions and machine code

hexinstructionmachine code
0 JnS X 0aaa
1 Load X 1aaa
2 Store X 2aaa
3 Add X 3aaa
4 Subt X 4aaa
5 Input 5000
6 Output 6000
7 Halt 7000
8 Skipcond X 8aaa
9 Jump X 9aaa
A Clear A000
B AddI X Baaa
C JumpI X Caaa
D LoadI X Daaa
E StoreI X Eaaa
F    
aaa indicates the value of X for skipcond,
  the address of X otherwise
Skipcond: 000 for <, 400 for =, 800 for >

IR: instruction register
PC: program counter
ACC: accumulator
MAR: memory address register
MBR: memory buffer register