← Years 7–8 Data & Information

8-bit binary numbers and the range 0 to 255

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.

Part of: 7-8 Digital Technologies: Representing data with binary — Module 9, IGCSE Computer Science 0478 — 1.1 Number Systems — Module 7, IGCSE Computer Science 0478 — 3.4 Network Hardware — Module 11

Understanding 8-bit binary numbers and the range 0 to 255 in Years 7–8 Data & Information

What it does: All eight bits are 1, so the total is 255, the biggest value in one byte. Each place value is double the one to its right, starting at 1 and going up to 128. 11111111 = 128+64+32+16+8+4+2+1 = 255. There are 256 different values, but because we start counting at 0 the largest is 255. The smallest byte is 00000000 = 0 and the largest is 11111111 = 255. Add the place values that have a 1: 8 + 4 + 1 = 13. The 1s are in the 128 and 1 places, so 128 + 1 = 129. Do not just read the digits as a decimal number.

Common mistakes: 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. 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'.

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This module's key terms are also in a printable crossword (Modules 9–45) and word search (Modules 9–80).

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Learning
Duo
What are the place values of an 8-bit binary number, from left to right?
8, 7, 6, 5, 4, 3, 2, 1128, 64, 32, 16, 8, 4, 2, 1
Matches
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.
Applying
Meanings
Term
8-bit binary: 128 64 32 16 8 4 2 1
Meaning
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.
Practice
place values: 128 64 32 16 8 4 2 1
Testing
Gaps
1 byte = bits
Check Answer
Spots
1Binary: 00001101
2Ones: 8 + 4 + 2

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Quick Questions

1. What are the place values of an 8-bit binary number, from left to right?
A. 128, 64, 32, 16, 8, 4, 2, 1 ✓
B. 8, 7, 6, 5, 4, 3, 2, 1
Each place value is double the one to its right, starting at 1 and going up to 128.
2. What is the largest number one byte (8 bits) can store?
A. 255 ✓
B. 256
11111111 = 128+64+32+16+8+4+2+1 = 255. There are 256 different values, but because we start counting at 0 the largest is 255.
3. Which range of whole numbers can a byte store?
A. 1 to 256
B. 0 to 255 ✓
The smallest byte is 00000000 = 0 and the largest is 11111111 = 255.
4. What is 00001101 in decimal?
A. 13 ✓
B. 11
Add the place values that have a 1: 8 + 4 + 1 = 13.
5. What is 10000001 in decimal?
A. 18
B. 129 ✓
The 1s are in the 128 and 1 places, so 128 + 1 = 129. Do not just read the digits as a decimal number.

Match the Pairs

10000000 → The 8-bit binary number for 128, because only the 128 place value is switched on
00001010 → The 8-bit binary number for 10, because the 8 and 2 place values are switched on
The largest number a byte can store, with every place value switched on (128+64+32+16+8+4+2+1) → 11111111
The smallest number a byte can store, with every place value switched off → 00000000
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.
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.

Key Term

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.

Fill in the Blanks

1. 1 byte = 8 bits
Hint: Type how many bits make up one byte.
2. 128 64 32 16 8 4 2 1
Hint: Type the missing place value between 4 and 1.
3. 11111111 = 128+64+32+16+8+4+2+1 = 255
Hint: Add every place value to find the largest number a byte can store.
4. 00001010 = 8 + 2 = 10
Hint: Type the place value of the second 1 in the byte.
5. Smallest byte: 00000000 = 0
Hint: Type the byte where every bit is off.

Spot the Error

Question 1
A Binary: 00001101
B Ones: 8 + 4 + 2
C Total = 13
Line 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.
Question 2
A Values: 256 128 64 32 16 8 4 2
B Binary: 10000001
C 128 + 1 = 129
Line 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'.
Question 3
A Binary: 11111111
B Bits in a byte: 8
C Largest value: 256
D Smallest value: 0
Line C — 11111111 adds 128+64+32+16+8+4+2+1, which is 255, not 256. The line should be 'Largest value: 255'.
Question 4
A A byte has 4 bits
B Smallest: 00000000 = 0
C Largest: 11111111 = 255
Line 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'.
Question 5
A Binary: 01000001
B Place values: 64 and 1
C Total = 64 + 1 = 66
Line C — 64 + 1 is 65, not 66. Add only the place values that have a 1. The line should be 'Total = 64 + 1 = 65'.

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