vault backup: 2025-01-09 13:21:59

education/computer engineering/ECE2700/Digital Hardware.md

@@ -27,8 +27,21 @@ 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 
+- 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 |
+| --------------- | --------- |
+| $857 / 2 = 428$ | $1$       |
+| $428 / 2 = 214$ | $0$       |
+| $214 / 2 = 107$ | $0$       |
+| $107 / 2 = 53$  | $1$       |
+| $53 / 2 = 26$   | $         |
+|                 |           |
 # Definitions
 - **Xtor** is an abbreviation for *transistor*
 - **Moore's Law** states that the number of transistors on a chip doubles every two years.