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education/computer engineering/ECE2700/Digital Hardware.md
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@ -24,7 +24,8 @@ $$ V(D) = d_{n-1} * 10^{n-1} + d_{n - 2} * 10^{n-2} + \cdots + d_1 * 10^1 + d_0
In a binary or base 2 number system, each digit can be a zero or one, called a *bit*. In a binary or base 2 number system, each digit can be a zero or one, called a *bit*.
$$ D = d_{n-1}d_{n-2} \cdots d_1 d_0 $$ $$ D = d_{n-1}d_{n-2} \cdots d_1 d_0 $$
To determine the integer value, a very similar formula can be used. To determine the integer value, a very similar formula can be used.
$$ V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 $$ $$ V(B) = b_{n-1} * 2^{n-1} + b_{n-2} * 2^{n-2} \cdots b_{1} * 2^1 + b_0 * 2^0 $$This formula can be generalized as:
*For radix *
- 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 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). - 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 - A nibble is 4 bits, and a byte is 8 bits