Micro-Operations Digital Logic and Computer Design by Ravinder Nath Rajotiya - December 11, 2022December 16, 20220 Introduction Internal organization of a digital system is defined by sequence of micro-operations it performs on the data stored in its registers. The general purpose digital computer is capable of executing various micro-operations and, in addition, can be instructed as to what specific sequence of operations it must perform. Now we define basic terminologies: A program is a set of instructions that specify the operations, operands, and the sequence by which the processing has to occur. A computer instruction is a binary code that specifies a sequence of micro-operations for the computer. Instruction code is a group of bits that instruct the computer to perform a specific operation that is usually divided into parts and the most basic part is the operation
Digital Computer Organization and controls Digital Logic and Computer Design by Ravinder Nath Rajotiya - December 7, 2022December 11, 20220 Stored Program organization The simplest way to organize a computer is to have one processor register and an instruction code format with two parts. The first part specifies the operation to be performed and the second specifies the address. The memory address tells the control where to find the operand in the memory. This operand is read from the memory and used as data to be operated on together with the data stored in the processor register. Figure below depicts this type of computer organization. Instructions are stored in one section of the memory and the operands or data in another. For example if we have a 4K x16 memory unit, it will require 12-bit address to access each memory word. The instruction
Logic Gates Digital Logic and Computer Design by Ravinder Nath Rajotiya - September 22, 20220 LOGIC GATES In this post we are going to learn about all the logic gates, their symbols, truth table and the logic equations. The different logic gates that will be covered are: 1. BUFFER 2. NOT 3. OR 4. AND 5. NAND 6. NOR 7. XOR 8. XNOR Binary Values: When only two possible states are to
Boolean Postulates and Theorem Digital Logic and Computer Design by Ravinder Nath Rajotiya - September 22, 2022December 16, 20220 BOOLEAN POSTULATES and THEOREM Boolean algebra was introduced by George Boole in 1854. Boolean algebra is used to perform binary and logical operations and differs in this respect from the ordinary algebra. Postulates of Boolean Algebra 1. Identity Law : A + 0 = A A.1 = A 2. Commutative Law: (A+B) = (B+A) A.B = B.A 3. Associative Law: A + (B + C) = (A + B) + C A.(B.C) = (A.B).C 4. Distributive Law: A . (B + C) = A.B + A.C A + (B.C) = (A + B). (A + C) 5. Complement Law: A+A’ = 1 A.A’ = 0 Boolean Algebra Theorems 1. Duality Theorem: It states that we can derive a Boolean relation from another Boolean relation by just : i. Changing the ‘.’ With a ‘+’
Number System Representation Digital Logic and Computer Design by Ravinder Nath Rajotiya - September 21, 2022December 29, 20220 Data Representation Data in a digital computer is written in binary using one of the following representations. Unsigned Magnitude Representation Signed Magnitude 1’s Complement 2’s Complement however the 2's complement is best suited for the arithmetic operations. These are explained as follows. 1. Unsigned Number Representation In this representation all the bits represent only the magnitude of the number without consideration to the sign of the number. Example: D7 D6 D5 D4 D3 D2 D1 D0 Value Minimum Value 0 0 0 0 0 0 0 0 0 Maximum Value 1 1 1 1 1 1 1 1 2N-1 =255 The range of the numbers that can be represented in this representation is 0 to 2N-1 For a 4-bit number the range will be = 0 to 24-1 = 0 to 15 For an 8-bit number the range will be = 0 to 28-1 = 0 to 255 · Note: We cannot represent signed number in