Question

2.1

a. Find the 16-bit 2’s complementary binary representation for the decimal number 1987.

b. Find the 16-bit 2’s complementary binary representation for the decimal number −1987.

What are the 16-bit 1’s and 2’s complements of the following binary numbers?

c. 10000

d. 100111100001001

Convert the decimal number 19557 to floating point. Use the format SEEMMMM. All digits are decimal. The exponent is stored excess-40 (not excess-50). The implied decimal point is at the beginning of the mantissa. The sign is 1 for a positive number, 7 for a negative number. Hint: Note carefully the number of digits in the mantissa What is the floating point representation for 0.0000019557

Answer 1

================================ANSWER===============================================

A ) -

1987 =  1024 + 512 + 256 + 128 + 64 + 2 + 1

= 2 ^10 + 2^9 + 2^8 + 2^7 + 2^6 + 2^1 + 2^0

= 0000 0111 1100 0011  

B ) -

1987 = 1111 1000 0011 1101 ( 2'S COM.)

c) - & D) -

Convert the decimal number 19557 to floating point -

1. convert number 19557 -

• 1st to Shift the decimal point
• making number: = .19557x10^5
• and a round-to-nearest method = .1956x10^5
• the number expressed == (NNN) NNN-NNNN

floating point representation for 0.0000019557

floating point representation of -0.0000019557 and floating point representation 19557 as same.

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