Binary Numbering System

8 Questions

Off and on, respectively

To make it easier to store and manipulate data electronically

Division

By multiplying each digit of the second number by each digit of the first, then summing the results

Each position is 2 times greater in weight than the preceding position

To perform arithmetic operations, store data, and communicate with hardware devices

Study Notes

Named after its base, which is 2
Has 2 digits: 0 and 1
Position values for a binary number are 2^x, where x is an exponent, and each position is twice the weight of the preceding one

Used extensively in digital electronics and computing due to ease of representation using switches (0 = "off", 1 = "on")
Allows for electronic storage and manipulation of data using digital circuits

Used for representing and manipulating large binary numbers or expressing memory addresses in a compact format
Computer programs and programming languages use number system concepts to perform arithmetic operations, store data, and communicate with hardware devices

Addition
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (write 0, carry 1 to the next higher bit)
Subtraction
- 0 - 0 = 0
- 1 - 0 = 1
- 1 - 1 = 0
- 0 - 1 = 1 with borrow from the next higher bit
Multiplication
- 0 * 0 = 0
- 0 * 1 = 0
- 1 * 0 = 0
- 1 * 1 = 1
- Multiply each digit of the second number by each digit of the first, then sum the results
Division
- Divide a dividend by a divisor to find a quotient and possibly a remainder
- Subtract in binary, bringing down the next digit

8 Questions