Section 7.4 Binary numbers
Digital computation uses the binary, or base-2, number system. In the binary number system, we will refer to bits rather than digits which are used in the decimal (base-10) system. Each digit in a base-10 number can assume any one of ten values (0-9) which is then multiplied by \(10^n\) where \(n\) is the number of digits to the left of the decimal point. For example, decimal number 1092 can be understood as \(1\times 10^3 + 0\times 10^2 + 9\times 10^1 + 2\times 10^0\text{.}\) Likewise, each bit in a binary number can take on one of two possible values (0 and 1) with these values multiplying a power of 2. So, the binary number 1011 can be understood as \(1\times 2^3 + 0\times 2^2 + 1\times 2^1 + 1\times 2^0\text{.}\) This means that the binary number 1011 represents 11 in decimal. Table 7.4.1 provides a list of all 4-bit binary numbers and their decimal counterparts.
Table 7.4.1. Binary to decimal equivalents for every 4-bit number.
| Binary | Decimal |
|---|---|
| 0000 | 00 |
| 0001 | 01 |
| 0010 | 02 |
| 0011 | 03 |
| 0100 | 04 |
| 0101 | 05 |
| 0110 | 06 |
| 0111 | 07 |
| 1000 | 08 |
| 1001 | 09 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
A binary number comprised of \(n\) bits has \(2^n\) possible values, and DISCUSS BINARY POINT (LIKE DECIMAL POINT)
