Converting a negative denary number to two's complement

Tip: Choose Save as PDF in the print dialog to download. Use A4 paper size.

Converting a negative denary number to two's complement

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. What is the FIRST step to write -6 in 8-bit two's complement?
A Write the positive value 6 in 8-bit binary: 00000110
B Write 6 in binary and put a minus sign in front of it
2. You have written 5 as 00000101. What do you do next to make -5?
A Add 1 to get 00000110
B Flip every bit to get 11111010
3. Which is -5 in 8-bit two's complement?
A 11111011
B 11111010
4. What is the last step when converting a negative number to two's complement?
A Add 1 to the flipped bits
B Subtract 1 from the flipped bits
5. Which is -3 in 8-bit two's complement?
A 11111100
B 11111101
B

Match the Pairs

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

Left columnRight column
100000101 -> 11111010 AAdd 1 to the flipped bits to finish the two's complement of -5
211111010 + 1 = 11111011 BThe student flipped the bits but forgot to add 1. The correct answer is 11111100 + 1 = 11111101.
3Check a two's complement answer by starting with -128 and adding the place values of the 1 bits CFlip every bit of 5 in 8-bit binary (0 becomes 1, 1 becomes 0)
4To write -10: 10 is 00001010, flip to 11110101, then add 1 D-128 + 64 + 32 + 16 + 8 + 2 + 1 = -5
5-3: 00000011 flipped = 11111100, so -3 = 11111100 EOnly the sign bit was changed. The correct method is to flip every bit of 00000101 to get 11111010, then add 1 to get 11111011.
6-5 = 10000101 (set the left bit to 1) F11110110
C

Definitions

flip the bits then add 1
D

Fill in the Blanks

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

1.
Step 1: 5 in 8 bits is ________
2.
Step 2: flip 00000101 to get ________
3.
Step 3: 11111010 + _ = 11111011
4.
3 = 00000011, flip: 11111100 add 1: 11111100 + 1 = ________
5.
11111011 = ____ + 64 + 32 + 16 + 8 + 2 + 1
E

Spot the Error

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

Question 1
A Number: -5
B Positive 5 = 00000101
C Flip bits: 11111110
D Add 1: 11111011
Question 2
A Convert -3
B 3 in binary: 00000110
C Flip: 11111100
D Add 1: 11111101
Question 3
A Step 1: write -6 as 10000110
B Step 2: flip to 11111001
C Step 3: add 1 = 11111010
Question 4
A Convert -4
B Flip 00000100 -> 11111010
C Add 1: 11111100
Question 5
A Rule: add 1, then flip bits
B -7: 7 is 00000111
C Flip: 11111000
D Add 1: 11111001

Answer Key

Converting a negative denary number to two's complement
Section A: Quick Questions
Q1
A — Write the positive value 6 in 8-bit binary: 00000110
Q2
B — Flip every bit to get 11111010
Q3
A — 11111011
Q4
A — Add 1 to the flipped bits
Q5
B — 11111101
Section B: Match the Pairs
Q1
00000101 -> 11111010 → Flip every bit of 5 in 8-bit binary (0 becomes 1, 1 becomes 0)
Q2
11111010 + 1 = 11111011 → Add 1 to the flipped bits to finish the two's complement of -5
Q3
Check a two's complement answer by starting with -128 and adding the place values of the 1 bits → -128 + 64 + 32 + 16 + 8 + 2 + 1 = -5
Q4
To write -10: 10 is 00001010, flip to 11110101, then add 1 → 11110110
Q5
-3: 00000011 flipped = 11111100, so -3 = 11111100 → The student flipped the bits but forgot to add 1. The correct answer is 11111100 + 1 = 11111101.
Q6
-5 = 10000101 (set the left bit to 1) → Only the sign bit was changed. The correct method is to flip every bit of 00000101 to get 11111010, then add 1 to get 11111011.
Section C: Definitions
Q1
flip the bits then add 1 — Write the positive value in 8-bit binary, flip every bit, then add 1. Example: 5 is 00000101, flip to 11111010, add 1 to get 11111011 (-5).
Section D: Fill in the Blanks
Q1
Step 1: 5 in 8 bits is 00000101
Q2
Step 2: flip 00000101 to get 11111010
Q3
Step 3: 11111010 + 1 = 11111011
Q4
3 = 00000011, flip: 11111100 add 1: 11111100 + 1 = 11111101
Q5
11111011 = -128 + 64 + 32 + 16 + 8 + 2 + 1
Section E: Spot the Error
Q1
C — Flipping 00000101 changes every bit (0 to 1, 1 to 0), giving 11111010. The broken line left the second-to-last bit as 1 when it should have flipped to 0, so only some bits were flipped.
Q2
B — The first step is to write the positive value in 8-bit binary. 3 is 00000011 (2 + 1). 00000110 is 6, so every step after it would be wrong.
Q3
A — Step 1 is to write the positive value, 6, in ordinary 8-bit binary: 00000110. Putting a sign bit on the front (10000110) is not how two's complement works.
Q4
B — Flipping 00000100 gives 11111011. The broken line flipped the last bit incorrectly, leaving it as 0 instead of changing it from 0 to 1.
Q5
A — The order matters. The rule is to flip every bit first and then add 1. Adding 1 first and then flipping gives a different, wrong answer.