Question

What decimal value does the 8-bit binary number 10011110 have if:

a) it is interpreted as an unsigned number?

b) It is on a computer using signed-magnitude representation?

c) It is on a computer using one’s complement representation?

d) It is on a computer using two’s complement representation?

Answer 1

a)
=> 10011110
=> 1x2^7+0x2^6+0x2^5+1x2^4+1x2^3+1x2^2+1x2^1+0x2^0
=> 1x128+0x64+0x32+1x16+1x8+1x4+1x2+0x1
=> 128+0+0+16+8+4+2+0
=> 158
Answer: 158

b)
10011110
since left most bit is 1, this number is negative number.
convert 0011110 to decimal
=> 0011110
=> 0x2^6+0x2^5+1x2^4+1x2^3+1x2^2+1x2^1+0x2^0
=> 0x64+0x32+1x16+1x8+1x4+1x2+0x1
=> 0+0+16+8+4+2+0
=> 30
Answer: -30

c)
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   10011110 is flipped to 01100001
01100001 in decimal
=> 01100001
=> 0x2^7+1x2^6+1x2^5+0x2^4+0x2^3+0x2^2+0x2^1+1x2^0
=> 0x128+1x64+1x32+0x16+0x8+0x4+0x2+1x1
=> 0+64+32+0+0+0+0+1
=> 97
Answer: -97

d)
II. Add 1 to 1's complement binary
01100001 + 1 = 01100010
III. Now convert this result to decimal value
=> 1100010
=> 1x2^6+1x2^5+0x2^4+0x2^3+0x2^2+1x2^1+0x2^0
=> 1x64+1x32+0x16+0x8+0x4+1x2+0x1
=> 64+32+0+0+0+2+0
=> 98
Answer: -98