The sign bit worth -128
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. In 8-bit two's complement, what is the place value of the leftmost bit?
2. Which row shows the 8-bit two's complement place values?
3. What does the binary pattern 10000000 represent in 8-bit two's complement?
4. What happens to the other seven bits in 8-bit two's complement?
5. What is 10000001 in 8-bit two's complement?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1-128 64 32 16 8 4 2 1 | A01000001 = 0 + 64 + 1 = 65 | |
| 210000000 | B11000001 = -128 + 64 + 1 = -63 | |
| 3When the leftmost bit is 1, add -128, then add the usual values of any other bits that are 1 | CThe leftmost bit was treated as +128. In two's complement it is worth -128, so the answer is -128 + 1 = -127. | |
| 4When the leftmost bit is 0, it adds nothing, so the number is positive and is read like normal binary | DThe 64 was added even though its bit is 0. Only bits that are 1 add their value, so 10000000 = -128. | |
| 510000001 = 128 + 1 = 129 | EThe place values of an 8-bit two's complement number, where the leftmost bit is worth -128 | |
| 610000000 = -128 + 64 = -64 | F-128, the smallest 8-bit two's complement number, because only the -128 bit is 1 |
C
Definitions
-128 64 32 16 8 4 2 1
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
Place values: ____ 64 32 16 8 4 2 1
2.
________ = -128
3.
10000001 = -128 + _ = -127
4.
11111111 = -128 + 127 = __
5.
01000000 = 0 + __ = 64
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
bits ← 10000001
B
sign ← 128
C
rest ← 1
D
OUTPUT sign + rest
Question 2
A
bits ← 10000000
B
sign ← -128
C
total ← sign + 127
D
OUTPUT total
Question 3
A
bits ← 11000000
B
sign ← -128
C
rest ← 64
D
total ← sign - rest
Question 4
A
places ← 128 64 32 16 8 4 2 1
B
FOR each bit that is 1
C
add its place value
Question 5
A
bits ← 10000100
B
total ← -127
C
total ← total + 4
D
OUTPUT total
Answer Key
The sign bit worth -128
Section A: Quick Questions
Q1
A — -128
Q2
B — -128 64 32 16 8 4 2 1
Q3
A — -128
Q4
A — They keep their usual values: 64, 32, 16, 8, 4, 2, 1
Q5
B — -127
Section B: Match the Pairs
Q1
-128 64 32 16 8 4 2 1 → The place values of an 8-bit two's complement number, where the leftmost bit is worth -128
Q2
10000000 → -128, the smallest 8-bit two's complement number, because only the -128 bit is 1
Q3
When the leftmost bit is 1, add -128, then add the usual values of any other bits that are 1 → 11000001 = -128 + 64 + 1 = -63
Q4
When the leftmost bit is 0, it adds nothing, so the number is positive and is read like normal binary → 01000001 = 0 + 64 + 1 = 65
Q5
10000001 = 128 + 1 = 129 → The leftmost bit was treated as +128. In two's complement it is worth -128, so the answer is -128 + 1 = -127.
Q6
10000000 = -128 + 64 = -64 → The 64 was added even though its bit is 0. Only bits that are 1 add their value, so 10000000 = -128.
Section C: Definitions
Q1
-128 64 32 16 8 4 2 1 — The 8-bit two's complement place values. The leftmost bit (the sign bit) is worth -128 when it is 1, and the other seven bits keep their usual values, so 10000000 = -128.Section D: Fill in the Blanks
Q1
Place values: -128 64 32 16 8 4 2 1Q2
10000000 = -128Q3
10000001 = -128 + 1 = -127Q4
11111111 = -128 + 127 = -1Q5
01000000 = 0 + 64 = 64Section E: Spot the Error
Q1
B — In 8-bit two's complement the leftmost bit is worth -128, not +128. The line should be sign ← -128, so the answer is -128 + 1 = -127.
Q2
C — The other seven bits of 10000000 are all 0, so they add nothing. The total is just the sign bit's value, so the line should be total ← sign, giving -128.
Q3
D — The other bits keep their usual positive values and are added to -128. It should be total ← sign + rest, giving -128 + 64 = -64.
Q4
A — The place values for 8-bit two's complement start with -128. The leftmost value must be -128, not 128.
Q5
B — A 1 in the leftmost bit adds -128, not -127. The line should be total ← -128, so the answer is -128 + 4 = -124.