Question

What decimal number does the bit pattern 10101100 represent if it is a:

• [1 pts] unsigned integer?
• [1 pts] sign-magnitude integer?
• [1 pts] two's complement integer?

What decimal number does the bit pattern 01010011 represent if it is a:

• [1 pts] unsigned integer?
• [1 pts] sign-magnitude integer?
• [1 pts] two's complement integer?

Answer 1

1. Given bit pattern : 10101100

a) if it is unsigned integer : 1 * 2⁷ + 1 * 2⁵ + 1 * 2³ + 1 * 2²

= 128 + 32 + 8 + 4 = 172

b) If it is a sign-magnitude integer : 10101100 -- MSB is 1. So it is a negative integer

0101100 = 1 * 2⁵ + 1 * 2³ + 1 * 2² = 32 + 8 + 4 = 46

= -46

c) If it is two's complement integer :  10101100 -- MSB is 1. So it is a negative number.

-- first invert the bits ====> 01010011

-- Now add 1 to it. =====> 01010011

+ 1

--------------------

01010100

magnitude of 01010100 = 1 * 2⁶+ 1 * 2⁴  + 1 * 2² = 64 + 16 + 4 = 84

So = -84.

2. Given bit pattern 01010011

a) if it is unsigned integer : 1 * 2⁶+ 1 * 2⁴  + 1 * 2¹ + 1 * 2⁰ = 64 + 16 + 2 + 1 = 83

b) If it is a sign-magnitude integer : 01010011 - MSB is 0. So it is a positive number.

So the integer = 83

c) If it is two's complement integer :  01010011 -- MSB is 0. So it is a Positive number.

So the integer = 83, because for positive 2's complement we dont need to do anything.

Answer 2

For the bit pattern 10101100:

1. Unsigned integer:

• Think of it as a plain binary number.

• Calculation: 1×2⁷ + 0×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 0×2⁰ = 128 + 0 + 32 + 0 + 8 + 4 + 0 + 0 = 172.

• 
  

2. Sign-magnitude integer:

• The first bit is the sign (1 = negative), the rest is the magnitude.

• Magnitude: 0101100 = 0×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 0×2⁰ = 0 + 32 + 0 + 8 + 4 + 0 + 0 = 44.

• Final value: -44.

• 
  

3. Two's complement integer:

• The first bit is negative, so invert the bits and add 1 to find the positive equivalent.

• Original: 10101100

• Invert: 01010011

• Add 1: 01010100 = 84

• Final value: -84.

---

For the bit pattern 01010011:

1. Unsigned integer:

• Plain binary number.

• Calculation: 0×2⁷ + 1×2⁶ + 0×2⁵ + 1×2⁴ + 0×2³ + 0×2² + 1×2¹ + 1×2⁰ = 0 + 64 + 0 + 16 + 0 + 0 + 2 + 1 = 83.

• 
  

2. Sign-magnitude integer:

• First bit is 0 = positive, the rest is the magnitude.

• Magnitude is the same as above: 83.

• Final value: +83.

• 
  

3. Two's complement integer:

• First bit is 0, so it's the same as the unsigned value.

• Final value: +83.

• 
  

Summary :-

• 10101100: Unsigned = 172, Sign-magnitude = -44, Two's complement = -84.

• 01010011: Unsigned = 83, Sign-magnitude = +83, Two's complement = +83.