Logic microoperations
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The document describes logic microoperations which are the basic logic functions performed on binary variables. It lists 16 logic microoperations corresponding to the 16 possible functions of two binary variables. These include operations like AND, OR, XOR, complement etc. It then discusses the hardware implementation of some logic microoperations using a multiplexer. It further explains various applications of logic microoperations like selective set, clear, complement etc. and how they can manipulate individual bits in a register. Shift microoperations and an arithmetic logic shift unit are also summarized.
Logic microoperations
- 1. Logic Microoperations Tarunpreet Bhatia CSED, Thapar University
- 2. LIST OF LOGIC MICROOPERATIONS • List of Logic Microoperations - 16 different logic operations with 2 binary variables. - n binary variables → functions 2 2 n • Truth tables for 16 functions of 2 variables and the corresponding 16 logic micro-operations Boolean Function Micro- Operations Name x 0 0 1 1 y 0 1 0 1 0 0 0 0 F0 = 0 F 0 Clear 0 0 0 1 F1 = xy F A B AND 0 0 1 0 F2 = xy' F A B’ 0 0 1 1 F3 = x F A Transfer A 0 1 0 0 F4 = x'y F A’ B 0 1 0 1 F5 = y F B Transfer B 0 1 1 0 F6 = x y F A B Exclusive-OR 0 1 1 1 F7 = x + y F A B OR 1 0 0 0 F8 = (x + y)' F A B)’ NOR 1 0 0 1 F9 = (x y)' F (A B)’ Exclusive-NOR 1 0 1 0 F10 = y' F B’ Complement B 1 0 1 1 F11 = x + y' F A B 1 1 0 0 F12 = x' F A’ Complement A 1 1 0 1 F13 = x' + y F A’ B 1 1 1 0 F14 = (xy)' F (A B)’ NAND 1 1 1 1 F15 = 1 F all 1's Set to all 1's
- 3. HARDWARE IMPLEMENTATION OF LOGIC MICROOPERATIONS 0 0 F = A B AND 0 1 F = AB OR 1 0 F = A B XOR 1 1 F = A’ Complement S1 S0 Output -operation Function table B A S S F 1 0 i i i 0 1 2 3 4 X 1 MUX Select
- 4. APPLICATIONS OF LOGIC MICROOPERATIONS •Logic microoperations can be used to manipulate individual bits or a portions of a word in a register •Consider the data in a register A. In another register, B, is bit data that will be used to modify the contents of A Selective-set A A + B Selective-complement A A B Selective-clear A A • B’ Mask (Delete) A A • B Clear A A B Insert A (A • B) + C Compare A A B
- 5. SELECTIVE SET •In a selective set operation, the bit pattern in B is used to set certain bits in A 1 1 0 0 At 1 0 1 0 B 1 1 1 0 At+1 (A A + B) •If a bit in B is set to 1, that same position in A gets set to 1, otherwise that bit in A keeps its previous value. •OR microoperation can be used to selectively set bits of a register.
- 6. SELECTIVE COMPLEMENT •In a selective complement operation, the bit pattern in B is used to complement certain bits in A 1 1 0 0 At 1 0 1 0 B 0 1 1 0 At+1 (A A B) •If a bit in B is set to 1, that same position in A gets complemented from its original value, otherwise it is unchanged. •The exclusive-OR microoperation can be used to selectively complement bits of a register.
- 7. SELECTIVE CLEAR •In a selective clear operation, the bit pattern in B is used to clear certain bits in A 1 1 0 0 At 1 0 1 0 B 0 1 0 0 At+1 (A A B’) •If a bit in B is set to 1, that same position in A gets set to 0, otherwise it is unchanged
- 8. MASK OPERATION •In a mask operation, the bit pattern in B is used to clear certain bits in A 1 1 0 0 At 1 0 1 0 B 1 0 0 0 At+1 (A A B) •If a bit in B is set to 0, that same position in A gets set to 0, otherwise it is unchanged
- 9. CLEAR OPERATION •In a clear operation, if the bits in the same position in A and B are the same, they are cleared in A, otherwise they are set in A. 1 1 0 0 At 1 0 1 0 B 0 1 1 0 At+1 (A A B) •It compares words in A and B and produces all 0’s result if the two numbers are equal. This operation is achieved by XOR microoperation.
- 10. INSERT OPERATION •An insert operation is used to introduce a specific bit pattern into A register, leaving the other bit positions unchanged •This is done as –A mask operation to clear the desired bit positions, followed by –An OR operation to introduce the new bits into the desired positions
- 11. –Example •Suppose you wanted to introduce 1010 into the low order four bits of A: 1101 1000 1011 0001 A (Original) 1101 1000 1011 1010 A (Desired) •1101 1000 1011 0001 A (Original) 1111 1111 1111 0000 Mask 1101 1000 1011 0000 A (Intermediate) 0000 0000 0000 1010 Added bits 1101 1000 1011 1010 A (Desired)
- 12. SHIFT MICROOPERATIONS •Shift microoperations are used for serial transfer of data. •The information transferred through the serial input determines the type of shift. There are three types of shifts –Logical shift –Circular shift –Arithmetic shift Serial input • A right shift operation • A left shift operation Serial input
- 13. LOGICAL SHIFT •In a logical shift the serial input to the shift is a 0. •A right logical shift operation: •A left logical shift operation: •In a Register Transfer Language, the following notation is used –shl for a logical shift left –shr for a logical shift right –Examples: •R2 shr R2 •R3 shl R3 0 0
- 14. CIRCULAR SHIFT •In a circular shift the serial input is the bit that is shifted out of the other end of the register. •A right circular shift operation: •A left circular shift operation: •In a RTL, the following notation is used –cil for a circular shift left –cir for a circular shift right –Examples: •R2 cir R2 •R3 cil R3
- 15. ARITHMETIC SHIFT •An arithmetic shift is meant for signed binary numbers (integer) •An arithmetic left shift multiplies a signed number by two •An arithmetic right shift divides a signed number by two •The main distinction of an arithmetic shift is that it must keep the sign of the number the same as it performs the multiplication or division •A right arithmetic shift operation: •A left arithmetic shift operation: 0 sign bit sign bit
- 16. ARITHMETIC SHIFT •An left arithmetic shift operation must be checked for the overflow 0 V Before the shift, if the leftmost two bits differ, the shift will result in an overflow •In a RTL, the following notation is used –ashl for an arithmetic shift left –ashr for an arithmetic shift right –Examples: •R2 ashr R2 •R3 ashl R3 sign bit
- 17. ARITHMETIC LOGIC SHIFT UNIT S3 S2 S1 S0 Cin Operation Function 0 0 0 0 0 F = A Transfer A 0 0 0 0 1 F = A + 1 Increment A 0 0 0 1 0 F = A + B Addition 0 0 0 1 1 F = A + B + 1 Add with carry 0 0 1 0 0 F = A + B’ Subtract with borrow 0 0 1 0 1 F = A + B’+ 1 Subtraction 0 0 1 1 0 F = A - 1 Decrement A 0 0 1 1 1 F = A TransferA 0 1 0 0 X F = A B AND 0 1 0 1 X F = A B OR 0 1 1 0 X F = A B XOR 0 1 1 1 X F = A’ Complement A 1 0 X X X F = shr A Shift right A into F 1 1 X X X F = shl A Shift left A into F Arithmetic Circuit Logic Circuit C C 4 x 1 MUX Select 0 1 2 3 F S3 S2 S1 S0 B A i A D A E shr shl i+1 i i i i+1 i-1 i i
- 18. Example Register A holds 8-bit operand 11011001. Determine the operand B and logic microoperation to be performed in order to change the value of A to a)01101101 b)11111101 A = 11011001 A = 11011001 B = 10110100 ⊕ B = 11111101 (OR) A’ = 01101101 A’ ← A ⊕ B A’ = 11111101 A’ ← AVB