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Lecture 4 Chap 5 Types

Lecture 4 Chap 5 Types. Instructors: Fu-Chiung Cheng ( 鄭福炯 ) Associate Professor Computer Science & Engineering Tatung University. Operator Precedence. Miscellaneous **, abs, not multiplying *, /, mod, rem sign +, - adding +, - shifting sll, srl, sla, sra, ror, rol

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Lecture 4 Chap 5 Types

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  1. Lecture 4 Chap 5 Types Instructors: Fu-Chiung Cheng (鄭福炯) Associate Professor Computer Science & Engineering Tatung University

  2. Operator Precedence Miscellaneous **, abs, not multiplying *, /, mod, rem sign +, - adding +, - shifting sll, srl, sla, sra, ror, rol relational =, /=, <, <=, >, >= logical and, or, nand, nor, xor, xnor

  3. Operator Precedence • Logical operators are the lowest precedence. • Logical operators have the same precedence • It is impossible to mix logic operators. • a <= b or c and d -- illegal • a <= (b or c) and d -- OK • nand and nor cannot be chained • y <= a nand b nand c -- illegal • y <= (a nand b) nand c -- OK • y <= a or b or c -- OK • A. nand and nor are non-associative operators • B. non-inverting operators are associative

  4. Shift operators • Don’t mix Shift operators • a sll 2 srl 2; -- illegal • (a sll 2) srl 2; -- OK use parentheses • (strip off the leftmost two bits of bus a) • shift > logical • if a sll 2 > 5 then … • if (a sll 2) > 5 then

  5. Signed + and - • a + -b; -- illegal. • -a + b; -- OK (-a)+b signed +,- > +,- • -a*b; -- OK -(a*b) signed +,- < *,/ • a + b*c; --OK a+(b*c); • -a mod b; -- OK -(a mod b); • a = 3 b=4 • -a mod 4 = -3 • (-a) mod 4 = 1 • a ** b ** c ==> a ** (b ** c)

  6. Boolean operators • Boolean expression are transferred to sum-of-prducts • form. • Example: • a nand b ==> not a or not b • a nor b ==> not a and not b • a xor b ==> (not a and b) or (a and not b) • a xnor b ==> (a and b) or (not a and not b) (equal)

  7. Comparison Operators • equality test: = and /= xnor gates • ordering test: <, <=, >, >= subtractor • 4-bit equality:

  8. Comparison Operators • 4-bit ordering tester a<b: use subtractor a-b • a<b if msb=1 • optimization can be achieved by removed the unused • subtractor outputs. • other ordering test conversion: • A. a >b ==> b<a • B. a >=b ==> not (a <b) • C. a <=b ==> not (b<a) • a <0: check the msb bit. • a>=0: check the msb bit.

  9. Array Comparison Operators • Array equality: if a’length /= b’length then a /= b • if a’length = b’length • Array inequality = • not (array equality).

  10. Array Comparison Operators • Array less-than: a(2 downto 0) < b(3 downto 0)

  11. Shift operators • Shift left logical 4 bit (sll 4):

  12. Shift operators • Shift right logical 4 bit (srl 4):

  13. Shift operators • Shift left arithemetic 4 bit (sla 4):

  14. Shift operators • Shift right 4 arithmetic bit (sra 4):

  15. Shift operators • rotate left 1 bit (rol 1):

  16. Shift operators • rotate right 1 bit (ror 1):

  17. Arithmetic operators: • + addition • - subtraction • + plus sign • - minus sign • * multiplication • / division • mod modulo arithmetic • rem remainder after division • ** exponentiation • abs absolute value

  18. Arithmetic operators: plus sign • Implement: wire (no circuitry).

  19. Arithmetic operators: minus sign • Implement: 2’s-complementor • A. 1’s complement • B. + 1. • Use ripple-borrow subtractors. • Half-Subtractor: • dif <= x xor bi; • bo <= x or bi; • Truth table:

  20. Arithmetic operators: minus sign • 4-bit 2’s-complementor:

  21. Arithmetic operators: abs • Implement: mux + two complementor.

  22. Arithmetic operators: adder • Implement: ripple-carry adder. • Full-Adder: • sum <= x xor y xor ci; • co <= (x and y) or (x and ci) • or (y and ci);

  23. Arithmetic operators: subtracter • Implement: • ripple-borrow subtracter. • Full-subtracter: • dif <= x xor y xor ci; • bo <= (not x and y) • or (not x and bi) • or (y and bi);

  24. Arithmetic operators: multiplier • Implement: array multiplier • see pp. 94 and 95

  25. Arithmetic operators: divisor • Not fully implementation, support only divide by 2^k • Implement: shifter (unsigned division by 2)

  26. Arithmetic operators: divisor • Not fully implementation, support only divide by 2^k • Implement: shifter + mux (signed division)

  27. Arithmetic operators: modulo • modulo is similar to division (not fully support). • Implement: wire (unsigned and unsigned modulo by 128)

  28. Arithmetic operators: remainder • Implement: mux + modulo

  29. Exponentiation operator: • Implement: only x**2 is allowed. • X**2 = x*x

  30. Concatenation operator: • conatenation operator allow an array to be built up • out of smaller arrays. • Implement: not circuitry required • Example: • signal a,b : std_logic_vector(15 downto 0); • signal z: std_logic_vector(31 downto 0); • … • z <= a & b;

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