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Quizzes > Mathematics > Basic Math & Arithmetic

Number System Conversion Quiz: Master Binary, Decimal & Hexadecimal

Ready for binary conversion practice? Take the quiz and sharpen your skills!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration showing binary code and decimal numbers framing quiz title on a dark blue background

This binary to decimal practice quiz helps you convert numbers between base 2 and base 10 quickly and with fewer mistakes. Work through short items in the practice set, switch to decimal-to-binary as needed, and use your score to spot gaps before an exam; for more, try extra drills.

Convert the binary number 1010 to its decimal equivalent.
5
10
12
8
The binary digits represent 2^3 through 2^0. 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal. This conversion is foundational to binary arithmetic and computer operations.
What is the decimal equivalent of the binary number 111?
9
6
8
7
Binary 111 equals 1×4 + 1×2 + 1×1 = 7 in decimal. Each bit weight halves as you move right. This is a basic building block in understanding binary systems.
Convert the decimal number 5 to its binary equivalent.
101
010
111
100
Divide 5 by 2 repeatedly to get remainders 1, 0, 1 from bottom to top. Thus 5 in binary is 101. This method works for any positive integer conversion.
Convert the binary number 1001 to its decimal equivalent.
9
13
11
8
1001 = 1×8 + 0×4 + 0×2 + 1×1 = 9. Identifying each bit's weight clarifies the total. Mastery of this is critical for digital electronics.
What is the binary equivalent of the decimal number 2?
100
10
010
11
2 in binary is 10 because it equals 1×2 + 0×1. This simple conversion underpins counting in base-2. It's used in computer memory addressing.
Convert the decimal number 0 to its binary equivalent.
0
1
00
000
Zero remains zero in any base, so its binary form is simply 0. This is a key concept for understanding null values in computing. No further digits are needed.
What is the binary representation of the decimal number 7?
100
101
111
110
7 = 4 + 2 + 1, so its binary form is 111. Each bit contributes to the total sum. This pattern recurs in binary addition.
Convert the binary number 0011 to its decimal equivalent.
2
4
3
1
0011 = 0×8 + 0×4 + 1×2 + 1×1 = 3. Leading zeros do not affect the value. This helps in byte-alignment tasks in computing.
Convert the binary number 1101 to its decimal equivalent.
13
12
14
11
1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13. Intermediate conversions like this are common in programming. Mastery ensures accurate data interpretation.
What is the binary equivalent of the decimal number 13?
1001
1110
1011
1101
13 /2 =6 R1, 6 /2=3 R0, 3 /2=1 R1, 1 /2=0 R1 gives 1101. This method scales to larger numbers.
What is the decimal value of the binary number 1000?
8
10
4
16
1000 in binary equals 1×2³ = 8. Recognizing powers of two is essential in system architecture.
Convert the decimal number 9 to its binary equivalent.
1010
0110
1001
0011
9 = 8 + 1, so bits for 2³ and 2? are set: 1001. This is widely used in network addressing.
What is the decimal equivalent of the binary fraction 0.1?
0.5
0.25
1.0
0.75
.1 in binary equals 1×(1/2) = 0.5. Binary fractions use negative powers of two. This is key in floating-point calculations.
What is the decimal equivalent of the binary fraction 0.001?
0.25
0.0625
0.375
0.125
.001? = 1×(1/8) = 0.125. Each position right of the point is 2?¹, 2?², etc. This concept underlies binary-coded decimals.
Convert the decimal number 6 to its binary equivalent.
011
100
110
101
6 = 4 + 2, so the bits are 1×2² + 1×2¹ + 0×2? = 110. This is used in control registers.
Which binary number represents the decimal number 15?
1011
1101
1110
1111
15 = 8+4+2+1, so binary is 1111. All lower-order bits are set. This appears often in bitmask operations.
Convert the binary fraction 101.101 to its decimal equivalent.
6.75
4.875
5.625
5.125
101? = 5, and .101? = 0.5 + 0 + 0.125 = 0.625. Combined value is 5.625. Fractional conversion uses negative powers of two.
What is the 8-bit two's complement representation of decimal -5?
11111101
11110101
11111001
11111011
Start with 00000101 for +5, invert bits to 11111010, then add 1 to get 11111011. Two's complement is standard for negative integers.
What is the result of adding the binary numbers 1011 and 1101?
10100
11110
10000
11000
Binary 1011 (11) + 1101 (13) = 24 decimal, which is 11000 in binary. Proper carry handling is key in binary addition.
Convert the binary number 11011011 to its decimal equivalent.
219
215
182
203
11011011 = 128+64+0+16+8+0+2+1 = 219. Each bit weight adds to the total. This is often used in byte-level operations.
Convert the decimal number 255 to an 8-bit binary number.
11111111
11111110
10000000
01111111
255 is the maximum value in an 8-bit field, so all bits are 1: 11111111. This is key in understanding color channels and masks.
What is the decimal equivalent of the binary number 10010?
20
16
18
22
10010 = 1×16 + 0×8 + 0×4 + 1×2 + 0×1 = 18. Recognizing bit positions simplifies large conversions.
Convert the binary fraction 111001.01 to its decimal equivalent.
57.5
57.25
56.25
58.125
111001? = 57, and .01? = 0.25, so total = 57.25. This combines integer and fractional conversions.
What is the two's complement of the 8-bit binary number 00101101?
10101101
11010011
11010101
11010010
Invert 00101101 to get 11010010, then add 1 to produce 11010011. This is how you represent negative values in binary.
In 16-bit two's complement, what decimal number does the binary 1111111111110101 represent?
-5
-11
5
11
Invert the bits to 0000000000001010 (10), add 1 to get 0000000000001011 (11), then apply negative sign = -11. Two's complement allows seamless negative arithmetic.
0
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Study Outcomes

  1. Understand the Binary Number System -

    Learn how to interpret binary digits by recognizing positional values and base-2 concepts essential for binary to decimal practice.

  2. Convert Binary to Decimal -

    Master step-by-step techniques to accurately translate binary numbers into their decimal equivalents.

  3. Convert Decimal to Binary -

    Apply proven decimal to binary practice methods to transform standard decimal numbers into binary form with precision and speed.

  4. Solve Binary Number Practice Problems -

    Engage with binary number practice problems to reinforce your skills through instant feedback and targeted challenges.

  5. Implement Efficient Conversion Strategies -

    Develop quick and reliable binary conversion practice techniques to tackle complex number system questions under timed conditions.

Cheat Sheet

  1. Positional Weights in Binary -

    Every binary digit represents a power of two, starting at 2^0 on the right (MIT OpenCourseWare). For example, 1101₂ = 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 13₝₀, so labeling each position's weight helps reinforce the concept when tackling binary number practice problems.

  2. Division-and-Remainder Method for Decimal to Binary -

    The standard algorithm repeatedly divides the decimal number by 2 and records remainders (referenced by Khan Academy). Converting 13 to binary gives remainders 1,0,1,1 read bottom-up: 1101₂, so practice this step-by-step for binary conversion practice and fluency.

  3. Grouping for Hexadecimal Conversions -

    Binary-to-hex conversion uses four-bit "nibbles" (IEEE Computer Society guideline), making it quick to translate between bases. For instance, 1010 1111₂ becomes AF₝₆ by converting each nibble: 1010 = A, 1111 = F, a trick useful in advanced binary to decimal practice.

  4. Understanding Two's Complement -

    Two's complement is the standard for signed binary (Computer Systems: A Programmer's Perspective, CMU). Invert all bits of 00000101 and add 1 to represent -5 as 11111011, so practice flipping and adding for negative values in binary numbers practice problems.

  5. Mnemonic Tricks and the 128 - 64 - 32 - 16 - 8 - 4 - 2 - 1 Table -

    Memorize the weights table "128 64 32 16 8 4 2 1" or use "Right To Left, Count Powers of Two" as a catchy phrase (University of Texas resource). Rehearsing this table speeds binary to decimal practice and decimal to binary practice, boosting speed and confidence.

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