Converting 8-bit two's complement to denary

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Converting 8-bit two's complement to denary

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?
A 128
B -128
2. The leftmost bit of an 8-bit two's complement number is 0. What does this tell you?
A The number is positive
B The number is negative
3. What is 00001101 in 8-bit two's complement?
A -13
B 13
4. What is 11110110 in 8-bit two's complement?
A -10
B 246
5. What is 10000101 in 8-bit two's complement?
A -123
B -5
B

Match the Pairs

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

Left columnRight column
100101101 A-128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = -1
211111111 B00110101 = 32 + 16 + 4 + 1 = 53
3A leftmost 1 means the number is negative, so start with -128 and add the other place values that have a 1 CLeftmost bit is 0, so it is positive: 32 + 8 + 4 + 1 = 45
4A leftmost 0 means the number is positive, so just add the place values that have a 1 D10001001 = -128 + 8 + 1 = -119
511110110 = 128 + 64 + 32 + 16 + 4 + 2 = 246 EThe 1 place value was added, but the rightmost bit is 0. Only -128, 4 and 2 have a 1 under them, so the answer is -128 + 4 + 2 = -122.
610000110 = -128 + 4 + 2 + 1 = -121 FThe leftmost place value was treated as +128. In 8-bit two's complement it is -128, so the answer is -128 + 64 + 32 + 16 + 4 + 2 = -10.
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.
____, 64, 32, 16, 8, 4, 2, 1
2.
If the leftmost bit is 0, the number is ________
3.
00101101 = 32 + 8 + 4 + 1 = __
4.
11110110 = -128 + 64 + 32 + 16 + 4 + 2 = ___
5.
10000011 = -128 + 2 + 1 = ____
E

Spot the Error

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

Question 1
A Values: 128 64 32 16 8 4 2 1
B Bits: 11110110
C -128+64+32+16+4+2 = -10
Question 2
A Binary: 0100110
B Leftmost 0: positive number
C 64+8+4+1 = 77
Question 3
A Binary: 10000011
B Leftmost 1: start at 128
C -128+2+1 = -125
Question 4
A Binary: 11111111
B Leftmost 1: start at -128
C -128+127 = 1
Question 5
A Binary: 10101010
B Values: -128 64 32 16 8 4 2 1
C -128+32+8+2
D Answer: 86

Answer Key

Converting 8-bit two's complement to denary
Section A: Quick Questions
Q1
B — -128
Q2
A — The number is positive
Q3
B — 13
Q4
A — -10
Q5
A — -123
Section B: Match the Pairs
Q1
00101101 → Leftmost bit is 0, so it is positive: 32 + 8 + 4 + 1 = 45
Q2
11111111 → -128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = -1
Q3
A leftmost 1 means the number is negative, so start with -128 and add the other place values that have a 1 → 10001001 = -128 + 8 + 1 = -119
Q4
A leftmost 0 means the number is positive, so just add the place values that have a 1 → 00110101 = 32 + 16 + 4 + 1 = 53
Q5
11110110 = 128 + 64 + 32 + 16 + 4 + 2 = 246 → The leftmost place value was treated as +128. In 8-bit two's complement it is -128, so the answer is -128 + 64 + 32 + 16 + 4 + 2 = -10.
Q6
10000110 = -128 + 4 + 2 + 1 = -121 → The 1 place value was added, but the rightmost bit is 0. Only -128, 4 and 2 have a 1 under them, so the answer is -128 + 4 + 2 = -122.
Section C: Definitions
Q1
-128, 64, 32, 16, 8, 4, 2, 1 — Add the place values with a 1 under them to get the denary value. A leftmost 1 means -128 is added: 11110110 = -128+64+32+16+4+2 = -10. A leftmost 0 means positive.
Section D: Fill in the Blanks
Q1
-128, 64, 32, 16, 8, 4, 2, 1
Q2
If the leftmost bit is 0, the number is positive
Q3
00101101 = 32 + 8 + 4 + 1 = 45
Q4
11110110 = -128 + 64 + 32 + 16 + 4 + 2 = -10
Q5
10000011 = -128 + 2 + 1 = -125
Section E: Spot the Error
Q1
A — In 8-bit two's complement the leftmost place value is -128, not 128. The line should be Values: -128 64 32 16 8 4 2 1.
Q2
A — An 8-bit number needs exactly 8 bits. 0100110 only has 7 and would not add up to 77. It should be Binary: 01001101.
Q3
B — When the leftmost bit is 1 the number is negative, so you start at -128, not +128. The line should read Leftmost 1: start at -128.
Q4
C — -128 plus 127 is -1, not 1. All eight 1s in two's complement give -1. The line should be -128+127 = -1.
Q5
D — -128+32+8+2 = -128+42 = -86. The answer is negative because the leftmost bit is 1. It should be Answer: -86.