← ACARA Digital Technologies Years 7–8

Most and least significant bit

The leftmost bit of a binary number. It has the biggest place value, so it changes the number the most. The rightmost bit is the least significant bit.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 13

Understanding Most and least significant bit in ACARA Digital Technologies Years 7–8

What it does: Changing the leftmost bit adds 8, taking 5 up to 13. Changing the rightmost bit only changes the value by 1. The least significant bit is 0, so the number is even. 1010 is 8 + 2 = 10, which is even. The most significant bit is the leftmost bit because it has the biggest place value. Place values start at 1 on the right and double each step as you move left. If the rightmost bit is 0, the number has no 1 to add. Every other place value is even, so the number is even.

Common mistakes: A 1 in the least significant bit (the rightmost bit) means the number is odd. 1011 is 11, which is odd. The line should say 'odd'. In a 5-bit number the leftmost bit (MSB) has the biggest place value, which is 16. A place value of 1 belongs to the rightmost bit (LSB).

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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
In the binary number 1001, which bit is the most significant bit (MSB)?
The rightmost 1The leftmost 1
Matches
The most significant bit of 0110 is the 0 on the right.
↓
The most significant bit is the leftmost bit, not the rightmost. In 0110 it is the 0 on the left.
Applying
Meanings
Term
most significant bit
Meaning
The leftmost bit of a binary number. It has the biggest place value, so it changes the number the most. The rightmost bit is the least significant bit.
Practice
=IF(MOD(B2,2)=1,"odd","even")
Testing
Gaps
Leftmost bit = significant bit (MSB)
Check Answer
Spots
3LSB = rightmost bit
4LSB is 1, so number is even

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Quick Questions

1. In the binary number 1001, which bit is the most significant bit (MSB)?
A. The rightmost 1
B. The leftmost 1 ✓
The most significant bit is the leftmost bit because it has the biggest place value.
2. In the binary number 0110, which bit is the least significant bit (LSB)?
A. The leftmost 0
B. The rightmost 0 ✓
The least significant bit is the rightmost bit. It has the smallest place value, which is 1.
3. Which statement is true for the 8-bit number 10000000?
A. The leftmost bit is worth 128 ✓
B. The leftmost bit is worth 1
In 8 bits the leftmost place value is 128. The rightmost place value is 1.
4. Where do you start when you work out place values (1, 2, 4, 8...) of a binary number?
A. From the right, with the smallest place value 1 ✓
B. From the left, with the smallest place value 1
Place values start at 1 on the right and double each step as you move left.
5. Why does changing the leftmost bit of 1000 change the number the most?
A. It has the biggest place value ✓
B. It is the first bit you type
The leftmost bit has the biggest place value, so flipping it changes the number by the largest amount.

Match the Pairs

1000 → The leftmost bit is 1, so it is the most significant bit. It is worth 8 and makes this number big.
0111 → The rightmost bit is 1, so it is the least significant bit. It is worth 1 and tells us the number is odd.
Flipping the leftmost bit of 0101 changes the number the most, because it has the biggest place value → 0101 -> 1101
The rightmost bit decides odd or even: 0 means the number is even → 1010 = 10 (even)
The most significant bit of 0110 is the 0 on the right. → The most significant bit is the leftmost bit, not the rightmost. In 0110 it is the 0 on the left.
1100 is odd because it starts with 1. → Odd or even depends on the rightmost bit, not the leftmost. 1100 ends in 0, so it is even (12).

Key Term

most significant bit
The leftmost bit of a binary number. It has the biggest place value, so it changes the number the most. The rightmost bit is the least significant bit.

Fill in the Blanks

1. Leftmost bit = most significant bit (MSB)
Hint: Type the word that describes the leftmost bit, the one with the biggest place value.
2. Rightmost bit = least significant bit (LSB)
Hint: Type the word that describes the rightmost bit, the one with the smallest place value.
3. In 8-bit binary, the left bit is worth 128
Hint: Type the place value of the leftmost bit in an 8-bit number.
4. 10111 ends in 1, so the number is odd
Hint: The least significant bit decides this. Type odd or even.
5. Place values from the right: 1, 2, 4, 8, 16
Hint: Each place value is double the one before it. Type the next place value.

Spot the Error

Question 1
A number = 1011
B MSB = leftmost bit
C LSB = rightmost bit
D LSB is 1, so number is even
Line D — A 1 in the least significant bit (the rightmost bit) means the number is odd. 1011 is 11, which is odd. The line should say 'odd'.
Question 2
A number = 10000
B MSB place value = 1
C LSB place value = 1
Line B — In a 5-bit number the leftmost bit (MSB) has the biggest place value, which is 16. A place value of 1 belongs to the rightmost bit (LSB).
Question 3
A number = 0110
B LSB = 0, so number is odd
C MSB = 0
Line B — A 0 in the rightmost bit (LSB) means the number is even. 0110 is 6, which is even. The line should say 'even'.
Question 4
A binary = 1000
B MSB = 1
C LSB = 1
D value = 8
Line C — The least significant bit is the rightmost bit. In 1000 the rightmost bit is 0, not 1. The line should be LSB = 0.
Question 5
A start = 0101
B flip the MSB to get 1101
C number changes by 1
Line C — 0101 is 5 and 1101 is 13, so the number changes by 8. The MSB has the biggest place value, so flipping it changes the number the most. It does not change it by just 1.

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