← Years 7–8 Data & Information

Converting a larger decimal number to binary

To write a number in 8-bit binary, go from 128 down to 1. If the place value fits in what is left, write 1 and subtract it. If not, write 0. Check by adding the place values.

Part of: 7-8 Digital Technologies: Representing data with binary — Module 10, IGCSE Computer Science 0478 — 1.1 Number Systems — Module 8

Understanding Converting a larger decimal number to binary in Years 7–8 Data & Information

What it does: The 1s are in the 128, 16, 4 and 2 places. Adding them gives 150, which matches the starting number. 100 - 64 = 36, 36 - 32 = 4, and 4 - 4 = 0. So the 64, 32 and 4 places get a 1 and the rest get a 0. 128 is smaller than 200, so it fits. Write 1 and subtract: 200 - 128 = 72. The subtraction method takes away each place value that fits, so the number left gets smaller. 45 = 32 + 8 + 4 + 1, which gives 00101101. The other answer adds up to 32 + 8 + 2 + 1 = 43.

Common mistakes: After taking away 128, only 22 is left. 64 is bigger than 22, so it does not fit. The line should say '64 does not fit: write 0'. Only 8 is left, so 32 does not fit. When a place value does not fit you write 0, not 1. The line should end with 'write 0'.

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Learning
Duo
You are converting 200 to 8-bit binary. What do you write for the 128 place?
0, because 128 is too big for 2001, because 128 fits into 200 (200 - 128 = 72 left)
Matches
150 = 1001011
↓
Only 7 digits were written, so a place value was left out. Every place from 128 down to 1 needs a 1 or a 0. The correct answer is 10010110.
Applying
Meanings
Term
subtract place values
Meaning
To write a number in 8-bit binary, go from 128 down to 1. If the place value fits in what is left, write 1 and subtract it. If not, write 0. Check by adding the place values.
Practice
150 - 128 = 22 -> 1
Testing
Gaps
Place values: 128, 64, 32, 16, , 4, 2, 1
Check Answer
Spots
2128 fits: write 1, left 22
364 fits: write 1, left 22

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Quick Questions

1. You are converting 200 to 8-bit binary. What do you write for the 128 place?
A. 0, because 128 is too big for 200
B. 1, because 128 fits into 200 (200 - 128 = 72 left) ✓
128 is smaller than 200, so it fits. Write 1 and subtract: 200 - 128 = 72.
2. After writing 1 for a place value that fits, what do you do next?
A. Subtract that place value from the number you have left ✓
B. Add that place value to the number you have left
The subtraction method takes away each place value that fits, so the number left gets smaller.
3. You are converting 45. What do you write for the 128 place?
A. 0, because 128 is bigger than 45 ✓
B. 1, because 128 is a place value in the table
A place value only gets a 1 if it fits into what is left. 128 does not fit into 45, so write 0.
4. Which is 45 in 8-bit binary?
A. 00101101 ✓
B. 00101011
45 = 32 + 8 + 4 + 1, which gives 00101101. The other answer adds up to 32 + 8 + 2 + 1 = 43.
5. You have 22 left while converting 150. What do you write for the 64 place?
A. 1, because there are still bits left to fill
B. 0, because 64 is bigger than 22 ✓
Only write 1 if the place value fits. 64 does not fit into 22, so write 0 and keep 22 for the next place.

Match the Pairs

200 - 128 = 72 → 128 fits into 200, so write 1 for the 128 place and 72 is left to convert
50 < 64, so write 0 → 64 does not fit into 50, so write 0 for the 64 place and keep 50 as it is
Check your answer by converting back: add the place values that have a 1 → 10010110 = 128+16+4+2 = 150
Write 100 in 8-bit binary: 64 and 32 and 4 fit, and the other place values get 0 → 100 = 01100100
150 = 1001011 → Only 7 digits were written, so a place value was left out. Every place from 128 down to 1 needs a 1 or a 0. The correct answer is 10010110.
100 = 11100100 → A 1 was written for 128, but 128 does not fit into 100. It should be 0, giving 01100100.

Key Term

subtract place values
To write a number in 8-bit binary, go from 128 down to 1. If the place value fits in what is left, write 1 and subtract it. If not, write 0. Check by adding the place values.

Fill in the Blanks

1. Place values: 128, 64, 32, 16, 8, 4, 2, 1
Hint: Type the missing place value. Each one is half of the one before it.
2. 200 - 128 = 72, so the first digit is 1
Hint: Type the largest place value in an 8-bit number, which is the first one that fits into 200.
3. 8 is less than 32, so the 32 place gets 0
Hint: Type the binary digit you write when the place value does not fit.
4. Check: 128 + 64 + 8 = 200
Hint: Type the decimal total you get by adding the place values that have a 1.
5. 200 in 8-bit binary is 11001000
Hint: Type all 8 digits, with 1s only under the place values 128, 64 and 8.

Spot the Error

Question 1
A Convert 150 to binary
B 128 fits: write 1, left 22
C 64 fits: write 1, left 22
D 32 does not fit: write 0
E 16 fits: write 1, left 6
Line C — After taking away 128, only 22 is left. 64 is bigger than 22, so it does not fit. The line should say '64 does not fit: write 0'.
Question 2
A Convert 200 to binary
B 128 fits: write 1, left 72
C 64 fits: write 1, left 8
D 32 does not fit: write 1
E 16 does not fit: write 0
F 8 fits: write 1, left 0
Line D — Only 8 is left, so 32 does not fit. When a place value does not fit you write 0, not 1. The line should end with 'write 0'.
Question 3
A Convert 77 to binary
B 128 does not fit: write 0
C 64 fits: write 1, left 23
D 32 does not fit: write 0
Line C — The subtraction is wrong. 77 - 64 = 13, not 23. The line should say 'left 13'.
Question 4
A Convert 45 to 8 bits
B 128 and 64 fit: write 11
C 32 fits: write 1, left 13
D 16 does not fit: write 0
E 8 fits: write 1, left 5
Line B — 45 is smaller than both 128 and 64, so neither fits. Both bits must be 0, so the line should say '128 and 64 do not fit: 00'.
Question 5
A Values: 256 128 64 32 16 8 4 2
B Start with the biggest: 128
C Go down to the smallest: 1
Line A — 8-bit place values go from 128 down to 1. This line starts at 256 and misses out 1. It should be 'Values: 128 64 32 16 8 4 2 1'.

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