Range of 8-bit two's complement
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. What is the range of an 8-bit two's complement integer?
2. Which 8-bit pattern is the largest positive two's complement number?
3. Which 8-bit pattern is the smallest two's complement number?
4. What does 11111111 represent in 8-bit two's complement?
5. What range does unsigned 8-bit binary give, compared with 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 | |
|---|---|---|
| 101111111 | A0 to 255 | |
| 210000000 | B-128 to 127 | |
| 3An 8-bit two's complement integer can store every whole number from -128 up to 127 | CThe largest positive 8-bit two's complement number, which is 127 | |
| 4Unsigned 8-bit binary, with no sign bit, stores a different range from two's complement | DThe smallest 8-bit two's complement number, which is -128 | |
| 5Range of 8-bit two's complement: -127 to 128 | EThe ends are the wrong way round. The range is -128 to 127, because the sign bit is worth -128 and the largest positive is 01111111 = 127. | |
| 611111111 = 255 in 8-bit two's complement | F255 is the unsigned value. In two's complement the sign bit is worth -128, so 11111111 = -128 + 127 = -1. |
C
Definitions
-128 to 127
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
01111111 in two's complement = ___
2.
10000000 in two's complement = ____
3.
11111111 in two's complement = __
4.
Unsigned 8-bit range: 0 to ___
5.
Largest positive: ________ = 127
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
bits ← 8
B
min ← -127
C
max ← 127
D
OUTPUT min, max
Question 2
A
// 8-bit two's complement
B
01111111 = 128
C
10000000 = -128
D
11111111 = -1
Question 3
A
// 8-bit two's complement
B
01111111 = 127
C
11111111 = -1
D
10000000 = 128
Question 4
A
unsigned ← 0 TO 255
B
signed ← -128 TO 127
C
values ← 2 ^ 7
D
OUTPUT values
Question 5
A
bits ← 8
B
count ← 2 * bits
C
low ← -(count DIV 2)
D
high ← count DIV 2 - 1
Answer Key
Range of 8-bit two's complement
Section A: Quick Questions
Q1
B — -128 to 127
Q2
A — 01111111 = 127
Q3
A — 10000000 = -128
Q4
A — -1
Q5
B — 0 to 255
Section B: Match the Pairs
Q1
01111111 → The largest positive 8-bit two's complement number, which is 127
Q2
10000000 → The smallest 8-bit two's complement number, which is -128
Q3
An 8-bit two's complement integer can store every whole number from -128 up to 127 → -128 to 127
Q4
Unsigned 8-bit binary, with no sign bit, stores a different range from two's complement → 0 to 255
Q5
Range of 8-bit two's complement: -127 to 128 → The ends are the wrong way round. The range is -128 to 127, because the sign bit is worth -128 and the largest positive is 01111111 = 127.
Q6
11111111 = 255 in 8-bit two's complement → 255 is the unsigned value. In two's complement the sign bit is worth -128, so 11111111 = -128 + 127 = -1.
Section C: Definitions
Q1
-128 to 127 — The range of an 8-bit two's complement integer: 10000000 is -128, 11111111 is -1 and 01111111 is 127. Unsigned 8-bit binary gives 0 to 255 instead.Section D: Fill in the Blanks
Q1
01111111 in two's complement = 127Q2
10000000 in two's complement = -128Q3
11111111 in two's complement = -1Q4
Unsigned 8-bit range: 0 to 255Q5
Largest positive: 01111111 = 127Section E: Spot the Error
Q1
B — The smallest 8-bit two's complement value is -128 (10000000), not -127. The line should be min ← -128.
Q2
B — 01111111 is the largest positive value, which is 127. 128 cannot be stored as a positive 8-bit two's complement number. It should be 01111111 = 127.
Q3
D — The sign bit is worth -128, so 10000000 is -128, not +128. It should be 10000000 = -128.
Q4
C — 8 bits give 2 ^ 8 = 256 different patterns, for both unsigned and two's complement. 2 ^ 7 is only 128. It should be values ← 2 ^ 8.
Q5
B — The number of patterns is 2 to the power of bits, not 2 multiplied by bits. 2 * 8 is only 16. It should be count ← 2 ^ bits, which gives 256.