Question

4. 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 ones complement representation? d) It is on a computer using twos complement representation?

 5. Given the following two binary numbers: 11111100 and 01110000.

 a) Which of these two numbers is the larger unsigned binary number? b) Which of these two is the larger when it is being interpreted on a computer using signed- two's complement representation? c) Which of these two is the smaller when it is being interpreted on a computer using signed- magnitude representation?

 6. Using a word" of 4 bits, list all of the possible signed binary numbers and their decimal equivalents that are representable in:

 a) Signed magnitude b) One's complement c) Two's complement

Answer 1

4)
a)
Converting from unsigned binary to decimal
=> 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)
Left most bit is 1. so, it's negative.
Now, let's convert rest of the bits 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
so, 10011110 from sign-magnitude to decimal is -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
II. Now convert this result to decimal value
=> 1100001
=> 1x2^6+1x2^5+0x2^4+0x2^3+0x2^2+0x2^1+1x2^0
=> 1x64+1x32+0x16+0x8+0x4+0x2+1x1
=> 64+32+0+0+0+0+1
=> 97
Answer: -97

d)
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
II. Add 1 to above result
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