Page 103 - Engineering Digital Design

74 CHAPTER 2 / NUMBER SYSTEMS, BINARY ARITHMETIC, AND CODES

(b) The 2's complement of 011011101.1101 2
(c) The 8's complement of 501.74s
(d) The 16's complement of AF3.C8i6
2.14 Represent the following numbers in IEEE normalized FPN 2 form:
(a) 1101011.1011 2
(b) +27.6875,0
(c) -145.500,0
2.15 Add the following binary additions and verify in decimal:
(a) 10+11
(b) 101+011
(c) 10111+01110
(d) 101101.11+011010.10
(e) 0.1100+1.1101
2.16 Carry out the following binary subtraction operations in 2's complement and verify
in decimal:
(a) 01100-00101
(b) 0111011-0011001
(c) 01001000-01110101
(d) 010001.0101-011011.1010
(e) 00.011010-01.110001
2.17 Repeat Problem 2.16 in 1's complement.
2.18 Carry out the following binary multiplication operations and verify in decimal:
(a) 11 xOlOl
(b) 11101 x 1111011
(c) 1001.10 x 11101.11
(d) 110.011 x 1101.0101
(e) 0.1101 x 0.01 111
2.19 Carry out the following complement multiplications and verify in decimal:
(a) 00000111 x -00001101
(b) HOx -11101 (A: = 5)
(c) -11.01 x 101.11 (k = 5)
(d) 111.111 x -1.101 (k = 6)
(Hint: Consider switching minuend and subtrahend operands if it yields less work.)

2.20 Find the quotient for each of the following division operations by using the binary
equivalent of the familiar "pencil-and-paper" method used in long division of decimal
numbers. Show work details.
(a) 1100+100
(b) 111111 + 1001
2
(c) 11001.1 +011.11 (Carry out quotient to the 2~ bit and give the remainder)
6
(d) 100 + 1010 (Carry out quotient to the 2~ bit and give remainder)