Binary Adder-Subtractor




The subtraction of binary numbers can be done most conveniently by means of complements as discussed in Sec. 3-2. Remember that the subtraction A - B can be done by taking the 2's complement of B and adding it to A. The 2's complement can be obtained by taking the 1' s complement and adding one to the least significant pair of bits. The 1's complement can be implemented with inverters and a one can be added to the sum through the input carry.

Binary Adder-Subtractor

 

 

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The addition and subtraction operations can be combined into one common circuit by including an exclusive-OR gate with each full-adder. A 4-bit adder-subtractor circuit is shown in Fig. 4-7. The mode input M controls the operation. When M = 0 the circuit is an adder and when M = 1 the circuit becomes a subtractor. Each exclusive-OR gate receives input M and one of the inputs of B. When M = 0, we have B a1 0 = B. The full-adders receive the value of B, the input carry is O, and the circuit performs A plus B. When M = 1, we have B a1 1 = B' and C0 = 1. The B inputs are all complemented and a 1 is added through the input carry. The circuit performs the operation A plus the 2's complement of B. For unsigned numbers, this gives A - B if A '" B or the 2's complement of (8 - A) if A < B. For signed numbers, the result is A - B provided that there Is no overflow.



Frequently Asked Questions

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Ans: To implement the add microoperation with hardware, we need the registers that hold the data and the digital component that performs the arithmetic addition. The digital circuit that forms the arithmetic sum of two bits and a previous carry is called a full-adder . view more..
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Ans: The operation of a memory unit was described in Sec. 2-7. The transfer of information from a memory word to the outside environment is called a read operation. view more..
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Ans: A bus system can be constructed with three-state gates instead of multiplexers. A three-state gate is a digital circuit that exhibits three states. Two of the states are signals equivalent to logic 1 and 0 as in a conventional gate. The third state is a high-impedance state. view more..
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Ans: The subtraction of binary numbers can be done most conveniently by means of complements as discussed in Sec. 3-2. Remember that the subtraction A - B can be done by taking the 2's complement of B and adding it to A. The 2's complement can be obtained by taking the 1' s complement and adding one to the least significant pair of bits. The 1's complement can be implemented with inverters and a one can be added to the sum through the input carry. view more..
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Ans: The increment microoperation adds one to a number in a register. For example, if a 4-bit register has a binary value 0110, it will go toO! II afterit is incremented. This microoperation is easily implemented with a binary counter view more..
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Ans: Logic microoperations specify binary operations for strings of bits stored in registers. These operations consider each bit of the register separately and treat them as binary variables. For example, the exclusive-OR microoperation with the contents of two registers . view more..
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Ans: There are 16 different logic operations that can be performed with two binary variables. They can be determined from all possible truth tables obtained with two binary variables as shown in Table 4-5. In this table, each of the 16 columns F0 through F15 represents a truth table of one possible Boolean function for the view more..
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Ans: The hardware implementation of logic rnicrooperations requires that logic gates be inserted for each bit or pair of bits in the registers to perform the required logic function. Although there are 16 logic rnicrooperations, most computers use only four-AND, OR, XOR (exclusive-OR), and complementfrom which all others can be derived. view more..
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Ans: Logic microoperations are very useful for manipulating individual bits or a portion of a word stored in a register. They can be used to change bit values, delete a group of bits, or insert new bit values into a register. view more..
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Ans: The selective-set operation sets to 1 the bits in register A where there are corresponding 1's in register B. It does not affect bit positions that have D's in B. The following numerical example clarifies this operation. view more..
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Ans: Shift rnicrooperations are used for serial transfer of data. They are also used in conjunction with arithmetic, logic, and other data-processing operations. The contents of a register can be shifted to the left or the right. At the same time that the bits are shifted, the first flip-flop receives its binary information from the serial input view more..
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Ans: Instead of having individual registers performing the microoperations directly, computer systems employ a number of storage registers connected to a common operational unit called an arithmetic logic unit, abbreviated ALU. view more..
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Ans: In this chapter we introduce a basic computer and show how its operation can be puter specified with register is defined by its internal transfer registers, statements. the limirlg The otganization and control of structure, the comand the set of instructions that It uses. The design of the computer is then carried out in detall. Although the basic computer presented in this chap view more..
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Ans: An instruction code is a group of bits that instruct the computer to perform a specific operation. It is usually divided into parts, each having its own particular interpretation. The most basic part of an instruction code is its operation part. The operation code of an instruction is a group of bits that define such operations as add, view more..
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Ans: 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 an address. The memory address tells the control where to find an operand in memory. This operand is read from memory and used as the data to be operated on together with the data stored in the processor register view more..
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Ans: In this chapter we introduce a basic computer and show how its operation can be puter specified with register is defined by its internal transfer registers, statements. the limirlg The otganization and control of structure, the comand the set of instructions that It uses. The design of the computer is then carried out in detall. Although the basic computer presented in this chapter is very small compared to commercial computers, It has the advantage of being simple enough so we can demonstrate the design process without too many complications. view more..
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Ans: It is sometimes convenient to use the address bits of an instruction code not as an address but as the actual operand. When the second part of an instruction code specifies an operand, the instruction is said to have an immediate operand. view more..
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Ans: Computer instructions are normally stored in consecutive memory locations and are executed sequentially one at a time. The control reads an instruction from a specific address in memory and executes it. It then continues by reading the next instruction in sequence and executes it, and so on. view more..




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