Computing Technology Inquiry
Bits, Bytes, and Boolean Algebra
date
Aug 2, 2023
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bits-bytes-and-boolean-algebra
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Public
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computer
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Post
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Computing Technology Inquiry
updatedAt
Aug 3, 2023 06:08 AM
What is BinaryBuffer gateTruth tableNot GateTruth table - it’s always going to be the oppositeAnd GateOR GateAND v.s NANDAND Gate and Not Gate = NAND Gate2 types of NAND Gate = NOT Gate2 Types of NAND Gate - all input a and input a,bOR v.s NORHow to write a function given block diagrams with AND & OR GatesHow to write a function of a multi-level circuit diagramHow to draw a block diagram given the functionIdentifying Sum of Products Expressions (POS)Identifying Product of Sums Expressions (POS)Identifying the number of product terms, sum terms, literals, variables, Minterms (standard product terms), and Maxterms(standard sum terms)
What is Binary
0 → off → F → 0 Volt
1 → on → T → 5 Volts (but something other than zero)
Buffer gate
- It looks like a triangle pointing towards the right.
- On the left point: input
- On the right point: output
- If we call input “a”, the output will also be the same.
Truth table
a | out |
1 | 1 |
0 | 0 |
Not Gate
- it looks like buffer gate but it has a circle in the front
- If the input is a, the output will be the complementary of a
Truth table - it’s always going to be the opposite
a | out |
0 | 1 |
1 | 0 |
⇒ Basically, if the input is in the off state, the output will be in an on state, and vice versa.
And Gate
- 2 inputs and 1 output
a | b | out |
0 | 0 | 0 |
a | b | out |
1 | 0 | 0 |
a | b | out |
0 | 1 | 0 |
a | b | out |
1 | 1 | 1 |
OR Gate
- It’s a+b for the or logic gate
a | b | out |
0 | 0 | 0 |
a | b | out |
1 | 0 | 1 |
a | b | out |
0 | 1 | 1 |
a | b | out |
1 | 1 | 1 |
AND v.s NAND
0’ = 1
1’ = 0
a | b | ab |
0 | 0 | 0 |
1 | 0 | 0 |
0 | 1 | 0 |
1 | 1 | 1 |
AND
Contrast ↔
a | b | ab |
0 | 0 | 1 |
1 | 0 | 1 |
0 | 1 | 1 |
1 | 1 | 0 |
NAND
AND Gate and Not Gate = NAND Gate
2 types of NAND Gate = NOT Gate
2 Types of NAND Gate - all input a and input a,b
a | a | (aa)’ |
0 | 0 | 1 |
1 | 1 | 0 |
a | b | (ab)’ |
0 | 0 | 1 |
1 | 0 | 1 |
0 | 1 | 1 |
1 | 1 | 0 |
OR v.s NOR
a | b | a+b |
0 | 0 | 0 |
1 | 0 | 1 |
0 | 1 | 1 |
1 | 1 | 1 |
a | b | (a+b)’ |
0 | 0 | 1 |
1 | 0 | 0 |
0 | 1 | 0 |
1 | 1 | 0 |
How to write a function given block diagrams with AND & OR Gates
How to write a function of a multi-level circuit diagram
How to draw a block diagram given the function
Identifying Sum of Products Expressions (POS)
Identifying Product of Sums Expressions (POS)
Identifying the number of product terms, sum terms, literals, variables, Minterms (standard product terms), and Maxterms(standard sum terms)
- One literal could be a product term