Question

Find the decimal equivalents for the following 8-bit two’s complement numbers.

a. 0010 0100 Decimal Equivalent ___________

b. 1010 1001 Decimal Equivalent ___________

c. 1100 0011 Decimal Equivalent ___________

d. 0101 0101 Decimal Equivalent ___________

Answer 1

Steps to Convert 2's Complement Binary Numbers to Decimal Numbers :

1.Finding the Magnitude of the Number (Positive or Negative) by considering the MSB ( Most Significant Bit) (Left most bit is called MSB

2.If MSB is 0 then the Magnitude of the number is Positive. Then directly convert it into Decimal representation using positional Weight Method.

3. If MSB is 1 then the Magnitude of the Number is Negative. Then follow the below steps

Finding the Decimal Value :

• Applying 1's complement to the given Number
• Add 1 to the result
• And Then convert the final result into decimal representation by using Positional Weight Methods.
• Apply the Sign (found in Step 1) and to resultant value to get decimal equivalents for the 8-bit two’s complement numbers.

a. 0010 0100

Step1 : The MSB bit is 0 (leftmost bit) . Hence it is a Positive Number.

Step 2: Therefore directly converting it into Decimal using the Positional Weight Method.

Positional Weights	27	26	25	24	23	22	21	20
Bits	0	0	1	0	0	1	0	0
value	0	0	32	0	0	4	0	0

Value = Positional weight x Data Bit (Like 1x 2⁵ = 32 )

Total value = (0 × 2⁷ + 0 × 2⁶ + 1 × 2⁵ + 0 × 2⁴ + 0 × 2³ + 1 × 2² + 0 × 2¹ + 0 × 2⁰)

= 32 + 4 = 36

The  Decimal Equivalent of 0010 0100  is + 36

b. 1010 1001

Step1 : The MSB bit is 1 (leftmost bit) . Hence it is a Negative Number

Step 2: (As the number is Negative We have to use separate method )

2's complement Number (Given)	1	0	1	0	1	0	0	1
1's complement form	0	1	0	1	0	1	1	0
Adding 1	+							1
Final Result	0	1	0	1	0	1	1	1

Converting Final Result into Decimal using the Positional Weight Method.

Positional Weights	27	26	25	24	23	22	21	20
Bits	0	1	0	1	0	1	1	1
value	0	64	0	16	0	4	2	1

Value = Positional weight x Data Bit (Like 1x 2⁵ = 32 )

Total value = (0 × 2⁷ + 1 × 2⁶ + 0 × 2⁵ + 1 × 2⁴ + 0 × 2³ + 1 × 2² + 1 × 2¹ + 1 × 2⁰)

= 64 + 16 + 4 + 2 + 1 = 87

Now apply negative sign to get Final result

The  Decimal Equivalent of  1010 1001 is - 87

c. 1100 0011

Step1 : The MSB bit is 1 (leftmost bit) .Hence it is a Negative Number

Step 2: (As the number is Negative We have to use separate method )

2's complement Number (Given)	1	1	0	0	0	0	1	1
1's complement form	0	0	1	1	1	1	0	0
Adding 1	+							1
Final Result	0	0	1	1	1	1	0	1

Converting Final Result into Decimal using the Positional Weight Method.

Positional Weights	27	26	25	24	23	22	21	20
Bits	0	0	1	1	1	1	0	1
value	0	0	32	16	8	4	0	1

Value = Positional weight x Data Bit (Like 1x 2⁵ = 32 )

Total value = (0 × 2⁷ + 0 × 2⁶ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰)

= 32 + 16 + 8 + 4 + 1 = 61

Now apply negative sign to get Final result

The  Decimal Equivalent of  1100 0011 is - 61

d. 0101 0101

Step1 : The MSB bit is 0 (leftmost bit) . Hence it is a Positive Number.

Step 2: Therefore directly converting it into Decimal using the Positional Weight Method.

Positional Weights	27	26	25	24	23	22	21	20
Bits	0	1	0	1	0	1	0	1
value	0	64	0	16	0	4	0	1

Value = Positional weight x Data Bit (Like 1x 2⁵ = 32 )

Total value = (0 × 2⁷ + 1 × 2⁶ + 0 × 2⁵ + 1 × 2⁴ + 0 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰)

= 64 + 16 + 4 + 1 = 85

The  Decimal Equivalent of 0101 0101 is + 85

If You Have Any Doubts. Please Ask Using Comments.

Have A Great Day!