16-bit binary place values
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. What is the place value of the leftmost bit in a 16-bit binary number?
2. Which is true about 16-bit place values?
3. What place value comes straight after 4096 when moving left?
4. The right-hand byte of a 16-bit number uses which place values?
5. What is the place value of the 9th bit from the right in a 16-bit number?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 132768 16384 8192 4096 2048 1024 512 256 | AThe largest 16-bit binary number, which is 65535 in denary | |
| 21111111111111111 | BThe place values of the left-hand byte (the top 8 bits) of a 16-bit binary number | |
| 3The right-hand byte of a 16-bit number uses the same place values as an 8-bit number | CThe largest 16-bit value is 65535, not 65536. 65536 is the number of different values, because 0 counts as one of them. | |
| 4Each place value is double the one to its right, so the place value left of 256 is 512 | D128 64 32 16 8 4 2 1 | |
| 532768 16384 8192 4096 2048 1024 512 128 256 | EThe place values are out of order. 256 must come before 128, because each place value is double the one on its right. | |
| 6Largest 16-bit value = 65536 | F256 x 2 = 512 |
C
Definitions
32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
32768 16384 ____ 4096 2048 1024 512 256
2.
Right-hand byte: ___ 64 32 16 8 4 2 1
3.
Largest 16-bit value: _____
4.
1000000000000000 = _____
5.
0000000100000000 = ___
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
bits = 16
B
top = 32768
C
next = top - 2
D
print(next)
Question 2
A
a = [32768, 16384, 8192, 4096]
B
b = [2048, 1024, 512, 256]
C
c = [128, 64, 36, 16]
D
d = [8, 4, 2, 1]
Question 3
A
bits = 16
B
values = 2 ** bits
C
print(values) # 65536
D
print(values + 1) # 65535
Question 4
A
place = 128
B
for i in range(8):
C
print(place)
D
place = place * 2
Question 5
A
place = 1
B
for i in range(8):
C
print(place)
D
place = place * 2
Answer Key
16-bit binary place values
Section A: Quick Questions
Q1
B — 32768
Q2
A — Each is double the one to its right
Q3
B — 8192
Q4
A — 128 64 32 16 8 4 2 1
Q5
A — 256
Section B: Match the Pairs
Q1
32768 16384 8192 4096 2048 1024 512 256 → The place values of the left-hand byte (the top 8 bits) of a 16-bit binary number
Q2
1111111111111111 → The largest 16-bit binary number, which is 65535 in denary
Q3
The right-hand byte of a 16-bit number uses the same place values as an 8-bit number → 128 64 32 16 8 4 2 1
Q4
Each place value is double the one to its right, so the place value left of 256 is 512 → 256 x 2 = 512
Q5
32768 16384 8192 4096 2048 1024 512 128 256 → The place values are out of order. 256 must come before 128, because each place value is double the one on its right.
Q6
Largest 16-bit value = 65536 → The largest 16-bit value is 65535, not 65536. 65536 is the number of different values, because 0 counts as one of them.
Section C: Definitions
Q1
32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1 — The 16 place values of a 16-bit binary number. Each is double the one on its right, and the right-hand byte uses 128 to 1. All 16 bits set to 1 make the largest value, 65535.Section D: Fill in the Blanks
Q1
32768 16384 8192 4096 2048 1024 512 256Q2
Right-hand byte: 128 64 32 16 8 4 2 1Q3
Largest 16-bit value: 65535Q4
1000000000000000 = 32768Q5
0000000100000000 = 256Section E: Spot the Error
Q1
C — Each place value is double the one on its right, so the next one down is half of 32768. It should be next = top // 2, which gives 16384, not top - 2.
Q2
C — The place values keep halving: 128, 64, 32, 16. The value 36 is not a power of 2, so the line should be c = [128, 64, 32, 16].
Q3
D — With all 16 bits set to 1 the largest value is 65535, which is one less than the 65536 possible patterns. It should be values - 1, not values + 1.
Q4
D — Moving right along the byte, each place value is half the previous one (128, 64, 32 ... 1). It should be place // 2, not place * 2.
Q5
B — A 16-bit number has 16 place values, so the loop must run 16 times: range(16). Using range(8) stops at 128 and misses the left-hand byte.