← ACARA Digital Technologies Years 7–8

Reading 101 in binary: digits, not a hundred and one

A small 2 after a number shows it is binary (base 2). Say it digit by digit: one zero one. It means five in decimal, not one hundred and one.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 14

Understanding Reading 101 in binary: digits, not a hundred and one in ACARA Digital Technologies Years 7–8

What it does: Adding the small 2 (base subscript) after 101 marks it as a base 2 number. Binary numbers are read digit by digit. 'One hundred and one' is how we say the decimal number 101. 101₂ has a 1 in the fours place and a 1 in the ones place: 4 + 0 + 1 = 5. The 1 is in the twos place and the 0 is in the ones place, so 10₂ is 2 in decimal. It is said 'one zero', not 'ten'. 110 on its own could be decimal or binary. The subscript 2 removes the doubt. Binary is base 2, so it only uses two digits: 0 and 1. A number like 25₂ is not valid.

Common mistakes: The small 2 after the number means base 2, so 101_2 is a binary number, not a decimal one. The line should read: 101_2 is a binary number. 101_2 is read as digits and is worth five in decimal, not one hundred and one. The line should be: decimal ← 5.

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Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

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This module's key terms are also in a printable crossword (Modules 189–203) and word search (Modules 189–236).

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Learning
Duo
How should you say the binary number 101 (written 101₂) out loud?
One hundred and oneOne zero one
Matches
Reading 101_2 aloud as 'one hundred and one'
↓
Binary numbers are not read as hundreds. The 2 subscript means base 2, so say 'one zero one' and its value is five.
Applying
Meanings
Term
101_2
Meaning
A small 2 after a number shows it is binary (base 2). Say it digit by digit: one zero one. It means five in decimal, not one hundred and one.
Practice
101_2 is said one zero one
Testing
Gaps
Binary five is written 101 in base
Check Answer
Spots
1101_2 is a decimal number
2Say it: one zero one

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Quick Questions

1. How should you say the binary number 101 (written 101₂) out loud?
A. One zero one ✓
B. One hundred and one
Binary numbers are read digit by digit. 'One hundred and one' is how we say the decimal number 101.
2. What does the small 2 in 101₂ tell you?
A. The number is multiplied by 2
B. The number is written in base 2 (binary) ✓
The small number after a number is the base. It tells you which counting system is being used, so 101₂ is binary.
3. What is the value of 101₂ in decimal?
A. 5 ✓
B. 101
101₂ has a 1 in the fours place and a 1 in the ones place: 4 + 0 + 1 = 5.
4. The binary number 10₂ is worth:
A. Ten
B. Two ✓
The 1 is in the twos place and the 0 is in the ones place, so 10₂ is 2 in decimal. It is said 'one zero', not 'ten'.
5. You see the number 11 with no small 2 next to it in a maths class. Which is the safer assumption?
A. It is decimal, so it is eleven ✓
B. It is binary, so it is three
With no base marked, a number is normally read as decimal. A small 2 (11₂) is what shows it is binary.

Match the Pairs

101_2 → A binary number written with a base subscript 2. Say it 'one zero one'. It equals 5 in decimal.
10_2 → The binary number 'one zero', which equals 2 in decimal, not ten.
Write the number 101 so people know it is binary, not one hundred and one → 101_2
Write the number 101 so people know it is decimal, meaning one hundred and one → 101_10
Reading 101_2 aloud as 'one hundred and one' → Binary numbers are not read as hundreds. The 2 subscript means base 2, so say 'one zero one' and its value is five.
10_2 = 10 → 10 in binary is two, not ten. The digits one and zero show 1 two and 0 ones, so 10_2 = 2.

Key Term

101_2
A small 2 after a number shows it is binary (base 2). Say it digit by digit: one zero one. It means five in decimal, not one hundred and one.

Fill in the Blanks

1. Binary five is written 101 in base 2
Hint: Type the base number that the small subscript shows for binary.
2. Say 101 base 2 digit by digit: one zero one
Hint: Type the word for reading each single symbol one at a time.
3. 10 in base 2 is 2 in decimal, not ten
Hint: Type the decimal value of binary 10: one group of the second place value and no ones.
4. 101 base 2 = 4 + 0 + 1 = 5
Hint: Type the place value of the leftmost digit in a three-digit binary number.
5. 101 in base 10 is one hundred and one
Hint: Type the base number that marks an ordinary decimal number.

Spot the Error

Question 1
A 101_2 is a decimal number
B Say it: one zero one
C Its decimal value is 5
Line A — The small 2 after the number means base 2, so 101_2 is a binary number, not a decimal one. The line should read: 101_2 is a binary number.
Question 2
A binary ← 101_2
B Read digit by digit: 1, 0, 1
C decimal ← 101
Line C — 101_2 is read as digits and is worth five in decimal, not one hundred and one. The line should be: decimal ← 5.
Question 3
A x ← 10_2
B Say it: ten
C x in decimal is 2
Line B — Binary numbers are said digit by digit, so 10_2 is said 'one zero', not 'ten'. It is worth two in decimal. The line should be: Say it: one zero.
Question 4
A Write 101 in base 2 as 101_10
B The small 2 is the base
C It means binary
Line A — The small number after the digits is the base. Base 2 needs a small 2, so it should be 101_2, not 101_10.
Question 5
A bits ← 1 1 0
B Say it: one hundred and ten
C 110_2 is six in decimal
Line B — Binary digits are read one at a time, so 110_2 is said 'one one zero'. It is not 'one hundred and ten'. The line should be: Say it: one one zero.

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