Binary is a base-2 number system that uses only two digits, 0 and 1, to represent all values. Each digit position represents a power of 2, and computers use binary because electronic circuits have exactly two states: on and off.
Counting with only two states: on/off, yes/no, 0/1. Each extra digit doubles the count.
Showing a random 20 of 50 problems.
Example 1
medium
Convert 11112 to decimal and explain why it equals 24−1.
Example 2
medium
Convert decimal 23 to binary.23
Example 3
easy
In binary, what is 1+1?
Example 4
hard
Convert decimal 100 to binary by repeatedly dividing by 2 and recording remainders.100 = 64 + 32 + 4 = 1100100₂
Example 5
easy
Convert the binary number 10012 to decimal.Find the decimal value: only the 8 and 1 columns are active
Example 6
medium
Halving a binary integer (discarding the remainder) corresponds to which simple bit operation?
Example 7
medium
Add the binary numbers 10112 and 01102.
Example 8
challenge
What decimal value is 111111112 (eight 1s), and why is this number significant?All 8 bits set: 128+64+32+16+8+4+2+1
Example 9
medium
Doubling a binary number is done by what simple operation?
Example 10
easy
What is the decimal value of 1112?
Example 11
medium
How many bits are needed to represent decimal 200?
Example 12
medium
Convert the decimal number 13 to binary using powers of 2.13
Example 13
medium
Convert 11012 to decimal.Read the decimal value of 1101₂ from the place-value grid
Example 14
medium
Convert decimal 19 to binary.19
Example 15
easy
Convert decimal 6 to binary.
Example 16
easy
How many digits does the binary number system use?
Example 17
medium
In binary, what is 1+1+1? Give the binary result.
Example 18
easy
Convert decimal 5 to binary.5
Example 19
medium
How many bits are needed to represent decimal 64?
Example 20
easy
What is the rightmost (position 0) place value in binary?