8-bit binary numbers and the range 0 to 255
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. What are the place values of an 8-bit binary number, from left to right?
2. What is the largest number one byte (8 bits) can store?
3. Which range of whole numbers can a byte store?
4. What is 00001101 in decimal?
5. What is 10000001 in decimal?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 110000000 | A00000000 | |
| 200001010 | BPlace values double each step: 128 64 32 16 8 4 2 1. They do not count up by 1. | |
| 3The largest number a byte can store, with every place value switched on (128+64+32+16+8+4+2+1) | C11111111 | |
| 4The smallest number a byte can store, with every place value switched off | DThe 8-bit binary number for 128, because only the 128 place value is switched on | |
| 5A byte can store 0 to 256 | EThe largest value is 255, not 256. 11111111 adds up to 255, and 0 to 255 is 256 different values. | |
| 6Place values: 1 2 3 4 5 6 7 8 | FThe 8-bit binary number for 10, because the 8 and 2 place values are switched on |
C
Definitions
8-bit binary: 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.
1 byte = _ bits
2.
128 64 32 16 8 4 _ 1
3.
11111111 = 128+64+32+16+8+4+2+1 = ___
4.
00001010 = 8 + _ = 10
5.
Smallest byte: ________ = 0
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
Binary: 00001101
B
Ones: 8 + 4 + 2
C
Total = 13
Question 2
A
Values: 256 128 64 32 16 8 4 2
B
Binary: 10000001
C
128 + 1 = 129
Question 3
A
Binary: 11111111
B
Bits in a byte: 8
C
Largest value: 256
D
Smallest value: 0
Question 4
A
A byte has 4 bits
B
Smallest: 00000000 = 0
C
Largest: 11111111 = 255
Question 5
A
Binary: 01000001
B
Place values: 64 and 1
C
Total = 64 + 1 = 66
Answer Key
8-bit binary numbers and the range 0 to 255
Section A: Quick Questions
Q1
A — 128, 64, 32, 16, 8, 4, 2, 1
Q2
A — 255
Q3
B — 0 to 255
Q4
A — 13
Q5
B — 129
Section B: Match the Pairs
Q1
10000000 → The 8-bit binary number for 128, because only the 128 place value is switched on
Q2
00001010 → The 8-bit binary number for 10, because the 8 and 2 place values are switched on
Q3
The largest number a byte can store, with every place value switched on (128+64+32+16+8+4+2+1) → 11111111
Q4
The smallest number a byte can store, with every place value switched off → 00000000
Q5
A byte can store 0 to 256 → The largest value is 255, not 256. 11111111 adds up to 255, and 0 to 255 is 256 different values.
Q6
Place values: 1 2 3 4 5 6 7 8 → Place values double each step: 128 64 32 16 8 4 2 1. They do not count up by 1.
Section C: Definitions
Q1
8-bit binary: 128 64 32 16 8 4 2 1 — A byte has 8 bits with place values 128 down to 1. Add the place values that are 1s. The smallest number is 0 and the largest is 11111111 = 255, so a byte stores 0 to 255.Section D: Fill in the Blanks
Q1
1 byte = 8 bitsQ2
128 64 32 16 8 4 2 1Q3
11111111 = 128+64+32+16+8+4+2+1 = 255Q4
00001010 = 8 + 2 = 10Q5
Smallest byte: 00000000 = 0Section E: Spot the Error
Q1
B — In 00001101 the 1s are in the 8, 4 and 1 places, not the 2 place. The line should be 'Ones: 8 + 4 + 1', which adds up to 13.
Q2
A — A byte's eight place values run from 128 down to 1. It does not start at 256 or leave out the 1. The line should be 'Values: 128 64 32 16 8 4 2 1'.
Q3
C — 11111111 adds 128+64+32+16+8+4+2+1, which is 255, not 256. The line should be 'Largest value: 255'.
Q4
A — A byte has 8 bits, which gives the eight place values from 128 down to 1. The line should be 'A byte has 8 bits'.
Q5
C — 64 + 1 is 65, not 66. Add only the place values that have a 1. The line should be 'Total = 64 + 1 = 65'.