Digital Arithmetic and Arithmetic Circuits, Lecture notes of Engineering

Download Digital Arithmetic and Arithmetic Circuits and more Lecture notes Engineering in PDF only on Docsity! Digital Arithmetic 1 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) • Signed Binary Number: A binary number of fixed length whose sign (+/–) is represented by one bit (usually MSB) and its magnitude by the remaining bits. • Unsigned Binary Number: A binary number of fixed length whose sign is not specified by a bit. All bits are magnitude and the sign is assumed +. Signed/Unsigned Binary Numbers Digital Arithmetic 2 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) • Sum: – Result of an Addition Operation of two (or more) binary numbers (operands). • Carry: – A digit (or bit) that is carried over to the next most significant bit during an n-Bit addition operation. • The carry bit is a 1 if the result was too large to be expressed in n bits. Unsigned Binary Arithmetic Digital Arithmetic 5 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) Signed Binary Numbers – 2 • True-Magnitude Form: – A form of signed binary whose magnitude bits are the TRUE binary form (not complements). Digital Arithmetic 6 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) True-Magnitude Form • 5-Bit Numbers Negative Sign (S = 1) • +25 = 011001 (Note sign bit (MSB) Sign = 0) • –25 = 111001 (Same as +25 with sign = 1) • +12 = 001100 • –12 = 101100 Digital Arithmetic 7 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) Signed Binary Addition (8-Bit) • Signed Addition Positive (S = 0) • Similar to binary addition with a sign bit. 1001 0110 1011 0100 75 1110 0001 30 Digital Arithmetic 10 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) • Used in MPU (PC) Arithmetic 2’s Complement Form 1000 1011 1 0111 1011 72- 1000 0100 72 0111 1011 1 0110 1100 57- 1001 0011 57 Digital Arithmetic 11 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) • Add 2’s Complement to Minuend. ResultfromBitCarryDiscard 111100001 111110111111101165 000001010000010180 ?6580 2’s Complement Subtraction 11111011 11110101165 0001010065 65 of compliment s2' Digital Arithmetic 12 Digital Arithmetic and Arithmetic Circuits (Chapter 7 Dueck) • 2’s Complement Negative Result (65 – 80 = ?) Negative Result Example )(15 1111 0000 )15(Result Final 1 1 Add 1110 0000Invert 0001 1111 0000 011 1 C.) s(2' 0000 1011 80- 0001 0100 0001 0100 65 1010