Padding binary with leading zeros

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Quick Questions

Shade in the A or B circle for each question.

1. Which is the 8-bit way to write the number 5 in binary?

A 00000101

B 10100000

2. Adding leading zeros to a binary number changes its value.

A True

B False

3. Do 101 and 00000101 mean the same number?

A No, 00000101 is bigger

B Yes, both are 5

4. Why do computers pad binary codes to a fixed length like 8 bits?

A So every code is the same size and is easy to separate and read

B So the number becomes bigger

5. Where do you add the extra 0s to pad 11 to 8 bits?

A On the left: 00000011

B On the right: 11000000

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
100000101		A01000001
20011		BThe number 5 written as an 8-bit binary number, with five leading zeros added to fill all 8 bits
3Leading zeros do not change the value of a binary number, so these two numbers are both 5		CThe zeros were added on the right instead of the left. That changes the value to 160. Padding must go on the left: 00000101.
4Fixed-length codes make every character the same size, so 'A' (65) is stored in 8 bits with a leading zero		D101 = 00000101
55 in 8 bits = 10100000		EThis has 6 bits, not 4, and the zeros are on the right. Padding 110 to 4 bits should give 0110.
66 in 4 bits = 110000		FThe number 3 written in 4 bits, with two leading zeros padding the binary number 11

Definitions

leading zeros

Fill in the Blanks

Complete each line of code by filling in the missing parts.

101 padded to 8 bits = _____101

00000101 and 101 both have the value _

Pad 11 to 4 bits: __11

Leading zeros do not change the _____

Each character is padded to 8 bits. 3 characters = 3 x 8 = __ bits

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A n = 5

B bits = format(n, "8b")

C print(bits)

Question 2

A n = 5

B bits = bin(n)[2:].zfill(3)

C print(bits)

Question 3

A width = 3

B code = "101"

C padded = code.zfill(width)

D print(padded)

Question 4

A code = 101

B zeros = "0" * (8 - len(code))

C print(zeros + code)

Question 5

A bits = "101"

B size = 8

C zeros = size - len(bits)

D padded = bits + "0" * zeros

E print(padded)

Answer Key

Padding binary with leading zeros

Section A: Quick Questions

A — 00000101

B — False

B — Yes, both are 5

A — So every code is the same size and is easy to separate and read

A — On the left: 00000011

Section B: Match the Pairs

00000101 → The number 5 written as an 8-bit binary number, with five leading zeros added to fill all 8 bits

0011 → The number 3 written in 4 bits, with two leading zeros padding the binary number 11

Leading zeros do not change the value of a binary number, so these two numbers are both 5 → 101 = 00000101

Fixed-length codes make every character the same size, so 'A' (65) is stored in 8 bits with a leading zero → 01000001

5 in 8 bits = 10100000 → The zeros were added on the right instead of the left. That changes the value to 160. Padding must go on the left: 00000101.

6 in 4 bits = 110000 → This has 6 bits, not 4, and the zeros are on the right. Padding 110 to 4 bits should give 0110.

Section C: Definitions

leading zeros — Extra 0s added at the left of a binary number to fill a fixed number of bits. They do not change its value: 101 and 00000101 both mean 5.

Section D: Fill in the Blanks

101 padded to 8 bits = 00000101

00000101 and 101 both have the value 5

Pad 11 to 4 bits: 0011

Leading zeros do not change the value

Each character is padded to 8 bits.
3 characters = 3 x 8 = 24 bits

Section E: Spot the Error

B — Without the 0 in the format code, the number is padded with spaces instead of zeros. It should be "08b" so 5 becomes 00000101.

B — Padding to a width of 3 leaves 101 unchanged. An 8-bit code needs zfill(8) to give 00000101.

A — The fixed length is 8 bits, so width must be 8. A width of 3 adds no leading zeros because 101 is already 3 bits long.

A — len() only works on a string, and 101 without quotes is a number. It should be code = "101" so the bits can be counted and padded.

D — The zeros must go on the left of the number as leading zeros. Putting them on the right gives 10100000, which is 160, not 5.