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')'
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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
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Marie instructions and machine code
hex | instruction | machine 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
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