3、Digital Logic Number Conversions, Arithmetic, and Signed Representations

Digital Logic Number Conversions, Arithmetic, and Signed Representations

1. Decimal Conversion

1.1 Whole Number Conversion

Converting the whole - number part of a decimal to another base involves successive division.
- Steps :
1. Divide the decimal number by the target base.
2. Record the remainder as the least - significant digit of the converted number.
3. Use the quotient from the previous step and divide it by the base again.
4. Repeat until the quotient is 0.

For example, to convert a decimal number to binary:
| Division Step | Quotient | Remainder |
| — | — | — |
| First | 11 ÷ 2 = 5 | 1 |
| Second | 5 ÷ 2 = 2 | 1 |
| Third | 2 ÷ 2 = 1 | 0 |
| Fourth | 1 ÷ 2 = 0