Converting a larger decimal number to binary

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Quick Questions

Shade in the A or B circle for each question.

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)

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

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

4. Which is 45 in 8-bit binary?

A 00101101

B 00101011

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

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1200 - 128 = 72		A64 does not fit into 50, so write 0 for the 64 place and keep 50 as it is
250 < 64, so write 0		B128 fits into 200, so write 1 for the 128 place and 72 is left to convert
3Check your answer by converting back: add the place values that have a 1		CA 1 was written for 128, but 128 does not fit into 100. It should be 0, giving 01100100.
4Write 100 in 8-bit binary: 64 and 32 and 4 fit, and the other place values get 0		D10010110 = 128+16+4+2 = 150
5150 = 1001011		EOnly 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.
6100 = 11100100		F100 = 01100100

Definitions

subtract place values

Fill in the Blanks

Complete each line of code by filling in the missing parts.

Place values: 128, 64, 32, 16, _, 4, 2, 1

200 - ___ = 72, so the first digit is 1

8 is less than 32, so the 32 place gets _

Check: 128 + 64 + 8 = ___

200 in 8-bit binary is ________

Spot the Error

Shade in the letter of the line that contains an 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

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

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

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

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

Answer Key

Converting a larger decimal number to binary

Section A: Quick Questions

B — 1, because 128 fits into 200 (200 - 128 = 72 left)

A — Subtract that place value from the number you have left

A — 0, because 128 is bigger than 45

A — 00101101

B — 0, because 64 is bigger than 22

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

Place values: 128, 64, 32, 16, 8, 4, 2, 1

200 - 128 = 72, so the first digit is 1

8 is less than 32, so the 32 place gets 0

Check: 128 + 64 + 8 = 200

200 in 8-bit binary is 11001000

Section E: Spot the Error

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'.

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'.

C — The subtraction is wrong. 77 - 64 = 13, not 23. The line should say 'left 13'.

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'.

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'.