3.1 KiB
Any poduct that contains a logic circuit is classified as digital hardware.
- Moore's Law states that the number of a transistors on a chip doubles every two years
- The International Technology Roadmap for Semiconductors (ITRS) forecasts technology, including the number of transistors on a chip
- Multiple integrated circuits can be connected using a printed circuit board, or PCB.
- Standard chips conform to an agreed upon standard for functionality and physical configuration. They are usually less than 100 transistors in size, and provide basic building blocks for logic.
- These chips are combined to form a larger logic circuit
- They were popular until the 1980s
- As ICs improved, it became inefficient space-wise to have separate chips for each logical building block
- The functionality of these chips is fixed, and they do not change.
Programmable Logic Devices
Programmable logic devices (PLDs) include a number of programmable switches that can configure the internal circuitry of a chip
- The most common type of PLD is a Field Programmable Gate Array (FPGA)
- FPGAs are widely available, but come with the drawback that they're limited in speed and performance
Application Specific Integrated Circuits
Application Specific Integrated Circuits (ASICs) have higher maximum performance and transistor density compared to FPGAs, but the cost of production is very high.
- A logic circuit is made of connected logic gates
Binary Numbers
In base 10, a value is expressed by an n-tuple with n digits
D = d_{n-1}d_{n-2} \cdots d_1 d_0 This represents the value
V(D) = d_{n-1} * 10^{n-1} + d_{n - 2} * 10^{n-2} + \cdots + d_1 * 10^1 + d_0 * 10^0 In a binary or base 2 number system, each digit can be a zero or one, called a bit.
D = d_{n-1}d_{n-2} \cdots d_1 d_0 To determine the integer value, a very similar formula can be used.
V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 - The base of a number is often notated in the format of
(n)_b, EG a base 10 number might be(14)_{10}, and a binary number might be(10)_2. - The least significant bit (LSB) is usually the right-most bit. The highest value bit, or the most significant bit (MSB).
- A nibble is 4 bits, and a byte is 8 bits
Conversions
Base 10 to Binary
Repeatedly divide by 2, and track the remainder.
As an example, the below table shows how one might convert from (857)_{10} to base 2.
| Equation | Remainder |
|---|---|
857 / 2 = 428 |
1 |
428 / 2 = 214 |
0 |
214 / 2 = 107 |
0 |
107 / 2 = 53 |
1 |
53 / 2 = 26 |
1 |
26 / 2 = 13 |
0 |
13 / 2 = 6 |
1 |
6 / 2 = 3 |
0 |
3 / 2 = 1 |
1 |
1 / 2 = 0 |
1 |
The final answer is 1101011001. The least significant bit is the remainder of the first division operation, and the most significant bit is the remainder of the last operation.
Definitions
- Xtor is an abbreviation for transistor
- Moore's Law states that the number of transistors on a chip doubles every two years.
- A tuple is a finite and ordered list of things