Answer
(a) 21
(b) -22
(c) -10
(d) 27
(e) -7
Work Step by Step
To convert two' s complement to decimal representation we use the following steps -
1. Note the first bit, if this is 1 then the number is negative otherwise positive or zero.
2. Flip all the bits.
3. Add 1 to the number
4. Convert to decimal like regular binary number and add the sign calculated in the step 1.
a. 010101
MSB = 0 → positive
Binary → Decimal:
0×32+1×16+0×8+1×4+0×2+1×1=16+4+1=21
Decimal = 21
b. 101010
MSB = 1 → negative
Find two’s complement: invert → 010101, add 1 → 010110
010110 = 16 + 4 + 2 = 22
Add negative sign → -22
Decimal = -22
c. 110110
MSB = 1 → negative
Invert → 001001, add 1 → 001010
001010 = 2 + 8 = 10
Add negative sign → -10
Decimal = -10
d. 011011
MSB = 0 → positive
Binary → Decimal: 0×32 + 1×16 + 1×8 + 0×4 + 1×2 + 1×1 = 16 + 8 + 2 + 1 = 27
Decimal = 27
e. 111001
MSB = 1 → negative
Invert → 000110, add 1 → 000111
000111 = 4 + 2 + 1 = 7
Add negative sign → -7
Decimal = -7
