Trace Through Conversions

Practice step-by-step number conversions

How to Use This Activity

Work through each conversion step by step. Enter your answer for each step, then check if you're correct before moving on. This helps you understand the process, not just get the final answer.

Exercise 1: Binary to Denary

Convert the binary number 10110101 to denary by filling in each place value.

128	64	32	16	8	4	2	1
1	0	1	1	0	1	0	1

Step 1: Which place values have a 1? (Enter values separated by +)

Step 2: Add these values together. What is 128+32+16+4+1?

Final Answer: 10110101 in denary is:

Exercise 2: Denary to Binary

Convert 217 to binary using the division method. Trace through each division step.

Step 1: 217 ÷ 2 = ? remainder ?

Step 2: 108 ÷ 2 = ? remainder ?

Step 3: 54 ÷ 2 = ? remainder ?

Step 4: 27 ÷ 2 = ? remainder ?

Step 5: 13 ÷ 2 = ? remainder ?

Step 6: 6 ÷ 2 = ? remainder ?

Step 7: 3 ÷ 2 = ? remainder ?

Step 8: 1 ÷ 2 = ? remainder ?

Step 9: Reading remainders from bottom to top gives:

Final Answer: 217 in binary is:

Exercise 3: Binary Addition

Add 01101011 + 00110101 in binary, tracking carries.

Carry:

Number 1: 0 1 1 0 1 0 1 1

Number 2: 0 0 1 1 0 1 0 1

Result:

Fill in the carry row and result row above, then click Check All

Is there a carry out of the MSB (leftmost bit)?

What decimal value is 01101011?

What decimal value is 00110101?

107 + 53 = 160, but the result shows 10100000. The 8-bit result without the overflow carry represents:

Note: In this case, there IS a carry out but the 8-bit result (10100000 = 160) is still correct because 107 + 53 = 160 which fits in 8 bits. An overflow error only occurs when the TRUE result exceeds 255.

Exercise 4: Hexadecimal to Denary

Convert E7 (hexadecimal) to denary.

Hex digits: 0-9 = 0-9, A=10, B=11, C=12, D=13, E=14, F=15

Step 1: What denary value does E represent?

Step 2: What denary value does 7 represent?

Step 3: E is in the 16s column, so E × 16 = ?

Step 4: 7 is in the 1s column, so 7 × 1 = ?

Step 5: Add the values: 224 + 7 = ?

Exercise 5: Binary to Hexadecimal

Convert 11110010 to hexadecimal.

Step 1: Split into two nibbles (4-bit groups). Left nibble:

Step 2: Right nibble:

Step 3: Convert left nibble 1111 to denary (8+4+2+1):

Step 4: What hex digit represents 15?

Step 5: Convert right nibble 0010 to denary:

Step 6: What hex digit represents 2?

Final Answer: 11110010 in hexadecimal is:

Exercise 6: Binary Shifts

Perform shifts on the binary number 00110100 (denary 52).

Part A: Left Shift by 1

Starting value: 00110100. Shift all bits LEFT by 1, adding 0 on the right:

What is 01101000 in denary?

Original was 52. Left shift by 1 multiplies by 2. Is 104 = 52 × 2?

Part B: Left Shift by 2

Starting value: 00110100. Shift all bits LEFT by 2:

What is 11010000 in denary?

Left shift by 2 multiplies by 4. Is 208 = 52 × 4?

Part C: Right Shift by 1

Starting value: 00110100. Shift all bits RIGHT by 1, adding 0 on the left:

What is 00011010 in denary?

Right shift by 1 divides by 2 (integer division). Is 26 = 52 ÷ 2?

Your Progress

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