Parsons Problems

Drag and drop steps into the correct order

How to Solve Parsons Problems

The steps for each conversion are shown in the wrong order. Drag them into the correct sequence to complete the conversion. This helps you understand the method, not just memorise answers.

Problem 1: Binary to Denary Conversion

Put these steps in the correct order to convert 10110110 from binary to denary.

Identify which place values have a 1: 128, 32, 16, 4, 2

Write out the binary place values: 128, 64, 32, 16, 8, 4, 2, 1

Add the place values: 128 + 32 + 16 + 4 + 2 = 182

Place each binary digit under its place value: 1,0,1,1,0,1,1,0

The answer is 182 in denary

Drop steps here in order:

Problem 2: Denary to Binary (Division Method)

Put these steps in the correct order to convert 200 from denary to binary using repeated division.

Continue dividing by 2 until the quotient is 0

Pad with leading zeros if needed to make 8 bits

Start with the denary number (200)

Read the remainders from bottom to top

Divide by 2 and record the remainder (0 or 1)

Drop steps here in order:

Problem 3: Binary Addition

Put these steps in the correct order to add two 8-bit binary numbers.

Move to the next column (left), including any carry

Start from the rightmost column (LSB)

Add the bits in the column: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1)

Write both numbers aligned by their place values

Check for overflow if there's a carry out of the MSB

Repeat until all columns are added

Drop steps here in order:

Problem 4: Hexadecimal to Denary

Put these steps in the correct order to convert C5 from hexadecimal to denary.

Convert each hex digit to its denary value: C=12, 5=5

Add the results: 192 + 5 = 197

Multiply by place values: 12 × 16 = 192, 5 × 1 = 5

Identify the place values: 16s and 1s columns

The answer is 197 in denary

Drop steps here in order:

Problem 5: Binary to Hexadecimal

Put these steps in the correct order to convert 11001010 from binary to hexadecimal.

Convert each nibble to denary: 1100=12, 1010=10

Split the binary number into 4-bit groups (nibbles)

Combine the hex digits: CA

Group from right: 1100 | 1010

Convert to hex digits: 12=C, 10=A

Drop steps here in order:

Problem 6: Denary to Hexadecimal

Put these steps in the correct order to convert 250 from denary to hexadecimal.

Convert results to hex: 15=F, 10=A

Divide by 16: 250 ÷ 16 = 15 remainder 10

Write as FA (16s digit first, then 1s digit)

Start with the denary number (250)

Quotient (15) is the 16s column, remainder (10) is the 1s column

Drop steps here in order:

Problem 7: Binary Left Shift

Put these steps in the correct order to perform a left shift by 2 on 00101100.

The result represents the original × 4 (since shift by 2 = ×2²)

Move all bits 2 positions to the left

Start with the original binary: 00101100 (44 in denary)

Fill empty positions on the right with zeros: 10110000

10110000 = 176 (which is 44 × 4)

Drop steps here in order:

Problem 8: Binary Right Shift

Put these steps in the correct order to perform a right shift by 1 on 01100100.

Fill empty position on the left with zero: 00110010

00110010 = 50 (which is 100 ÷ 2)

Start with the original binary: 01100100 (100 in denary)

The result represents the original ÷ 2

Move all bits 1 position to the right (rightmost bit is lost)

Drop steps here in order:

Your Progress

Problem 1: Not attempted

Problem 2: Not attempted

Problem 3: Not attempted

Problem 4: Not attempted

Problem 5: Not attempted

Problem 6: Not attempted

Problem 7: Not attempted

Problem 8: Not attempted

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