Practice Binary in CS Thinking
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
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
mediumConvert to decimal and explain why it equals .
Example 2
mediumConvert decimal 23 to binary. 23 = 16 + 4 + 2 + 1 = 10111₂
Example 3
easyIn binary, what is ?
Example 4
hardConvert decimal 100 to binary by repeatedly dividing by 2 and recording remainders. 100 = 64 + 32 + 4 = 1100100₂
Example 5
easyConvert the binary number to decimal. Find the decimal value: only the 8 and 1 columns are active
Example 6
mediumHalving a binary integer (discarding the remainder) corresponds to which simple bit operation?
Example 7
mediumAdd the binary numbers and .
Example 8
challengeWhat decimal value is (eight 1s), and why is this number significant? All 8 bits set: 128+64+32+16+8+4+2+1 = 255
Example 9
mediumDoubling a binary number is done by what simple operation?
Example 10
easyWhat is the decimal value of ?
Example 11
mediumHow many bits are needed to represent decimal 200?
Example 12
mediumConvert the decimal number 13 to binary using powers of 2. 13 = 8 + 4 + 1 = 1101₂
Example 13
mediumConvert to decimal. Read the decimal value of 1101₂ from the place-value grid
Example 14
mediumConvert decimal 19 to binary. 19 = 16 + 2 + 1 = 10011₂
Example 15
easyConvert decimal 6 to binary.
Example 16
easyHow many digits does the binary number system use?
Example 17
mediumIn binary, what is ? Give the binary result.
Example 18
easyConvert decimal 5 to binary. 5 = 4 + 1 = 101₂
Example 19
mediumHow many bits are needed to represent decimal 64?
Example 20
easyWhat is the rightmost (position 0) place value in binary?