WorksheetsQuiz on Number Systems and Codes
Total questions: 14
Worksheet time: 22mins
Which of the following binary numbers, when converted to decimal, gives the same value as hexadecimal '3A'?
00111011
00111010
01101000
11111010
Analyze and choose the correct statement about the decimal equivalents of (1011)₂ and (11)₈.
Both are equal
Binary is greater
Octal is greater
Cannot be compared
Among the following, which binary pattern is not valid as a BCD representation?
0101
1000
1011
0010
Choose the most efficient method to convert (145)₁₀ to hexadecimal.
Convert to binary, then to hex
Divide by 16 and use remainders
Multiply by 16
Convert to octal and then to hex
When comparing Gray code and binary code sequences, which characteristic makes Gray code more suitable for mechanical systems?
More compact format
Lower memory usage
Single-bit variation between successive values
Faster processing
Which of the following operations shows an overflow in 4-bit 2's complement addition?
0101 + 0010
1100 + 1000
1001 + 0110
0110 + 0100
Analyze this: You subtract (13)₁₀ from (7)₁₀ using 2's complement. What is the correct result in 8-bit binary?
11111100
00000110
00000011
11111101
Which of the following binary subtraction operations is incorrect when done using 2's complement?
0110 - 0011 = 0011
0101 - 0101 = 0000
1000 - 0010 = 0110
0110 - 1001 = 1111
Identify the key difference when using 1's complement instead of 2's complement in binary subtraction.
Sign bit is lost
No end-around carry in 1's complement
Result is less accurate
Requires an end-around carry
You analyze the result of binary addition: 1111 + 0001. In 4-bit arithmetic, what can you conclude?
Correct result
Overflow occurred
Underflow occurred
Sign bit ignored
Which of the following codes is not self-complementing?
Excess-3
2421
5211
BCD
Analyze why Gray code is preferable in rotary encoders over binary code.
Binary is complex
Gray code uses fewer bits
Less chance of multiple transition errors
Easier to decode
Two Gray code numbers differ by two bits. What does this indicate?
Code error
Hardware failure
More than one step moved
Noise in transmission
A student uses 1's complement subtraction and gets the result 11110000. What should be done to correct it?
Add 1 to result
Flip the bits again
Subtract from 0
Perform XOR
