Converting numbers from 0 to 127 using seven place values
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. What is the largest whole number you can write using seven binary places?
2. Which is 100 written in seven-place binary?
3. What is 1010101 as a decimal number?
4. Which place values add up to 45?
5. To convert 70, which place value do you try first?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 11111111 | ASeven 1s add up to 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127, not 128. The largest 7-bit number is 127. | |
| 21100100 | BThe 1s are under 64 and 16, which add up to 80, not 40. Forty is 32 + 8, so it should be 0101000. | |
| 3Write 75 with seven place values: 64 + 8 + 2 + 1 = 75 | CThe number 100, because 64 + 32 + 4 = 100 | |
| 4Work down from 64 to write 50: no 64, then 32, 16 and 2 add up to 50 | D0110010 | |
| 540 = 1010000 | EThe largest 7-bit number: 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127 | |
| 61111111 = 128 | F1001011 |
C
Definitions
64 32 16 8 4 2 1
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
Place values: __ 32 16 8 4 2 1
2.
100 = 64 + 32 + 4
100 in binary is _______
3.
1111111 = 64+32+16+8+4+2+1 = ___
4.
50 is less than 64,
so the 64 place gets a _
5.
Largest 7-bit number: _______ = 127
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
Places: 64 32 16 8 4 2 1
B
100 - 64 = 46, so 64 gets 1
C
36 - 32 = 4, so 32 gets 1
D
4 needs only the 4 place
E
Answer: 1100100
Question 2
A
Places: 64 32 16 8 4 2 1
B
77 - 64 = 13, so 64 gets 1
C
13 - 8 = 6, so 8 gets 1
D
5 - 4 = 1, so 4 gets 1
E
1 - 1 = 0, so 1 gets 1
F
Answer: 1001101
Question 3
A
Binary: 1010101
B
Places: 64 32 16 8 4 2 1
C
Add: 64 + 32 + 4 + 1
D
Total: 64+16+4+1 = 85
Question 4
A
Largest 7-bit number: 1111110
B
64+32+16+8+4+2+1 = 127
C
So 7 bits store 0 to 127
Question 5
A
Places: 64 32 16 8 4 2 1
B
45 < 64, so the 64 place is 1
C
45 - 32 = 13, so 32 gets 1
D
13 = 8 + 4 + 1
E
Answer: 0101101
Answer Key
Converting numbers from 0 to 127 using seven place values
Section A: Quick Questions
Q1
A — 127, written as 1111111
Q2
B — 1100100 (64+32+4)
Q3
A — 85
Q4
A — 32 + 8 + 4 + 1
Q5
B — 64, the biggest value that fits in 70
Section B: Match the Pairs
Q1
1111111 → The largest 7-bit number: 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127
Q2
1100100 → The number 100, because 64 + 32 + 4 = 100
Q3
Write 75 with seven place values: 64 + 8 + 2 + 1 = 75 → 1001011
Q4
Work down from 64 to write 50: no 64, then 32, 16 and 2 add up to 50 → 0110010
Q5
40 = 1010000 → The 1s are under 64 and 16, which add up to 80, not 40. Forty is 32 + 8, so it should be 0101000.
Q6
1111111 = 128 → Seven 1s add up to 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127, not 128. The largest 7-bit number is 127.
Section C: Definitions
Q1
64 32 16 8 4 2 1 — The seven binary place values. Put a 1 under each value you need and a 0 under the rest to write any whole number from 0 to 127. Check by adding them back up. 1111111 = 127.Section D: Fill in the Blanks
Q1
Place values: 64 32 16 8 4 2 1Q2
100 = 64 + 32 + 4
100 in binary is 1100100Q3
1111111 = 64+32+16+8+4+2+1 = 127Q4
50 is less than 64,
so the 64 place gets a 0Q5
Largest 7-bit number: 1111111 = 127Section E: Spot the Error
Q1
B — 100 - 64 is 36, not 46. Subtracting wrongly would give the wrong remainder and the wrong binary number. The line should be 100 - 64 = 36.
Q2
C — 13 - 8 is 5, not 6. The remainder 5 is then used for the 4 place and the 1 place. The line should be 13 - 8 = 5.
Q3
C — In 1010101 the 32 place has a 0, so 32 must not be added. The 1s are under 64, 16, 4 and 1, so the line should be Add: 64 + 16 + 4 + 1.
Q4
A — The largest 7-bit number has a 1 in every place, including the 1 place. It is 1111111, which equals 127. 1111110 is only 126.
Q5
B — 45 is smaller than 64, so 64 does not fit into 45. The 64 place must be 0, not 1.