Yes, that would be the case.In other words, instead of ((AB)'+(CD)'), would the answer be ((AB)'+(CD)')' ?
This is because it is easier to create a NAND gate than most others...As a little aside. In the early days of the TTL logic. The 7400 gate costed less than others gates. So I am told is was cost effective(to some limit) to at least try to just use as many NAND gates as possible. But still to day. It is a quite common question on test and exams. To ask for a specific boolean algebra function. To be made just with NAND gates
Yes - the name of the file doesn't match the diagram contained therein.Sorry bertus, your drawing just confused me further, but thanks for trying.
Given the resolution to another question I posted, I obviously missed the small circles at the ends of the gates. Apparently these invert the values.
The image is called ((AB)'+(CD)'), something we couldn't see when taking the test. One thing I'm still confused about: Since there are three small inversion circles, shouldn't there be a third ' sign in the equation?
In other words, instead of ((AB)'+(CD)'), would the answer be ((AB)'+(CD)')' ?
Many thanks
Actually, this is multiplication:The dot in Boolean means to AND, not to multiply as in normal algebra. Example: A . B = Y means input A AND input B equals output Y.
This is addition, however, it isn't decimal addition. This is binary addition, where only 1 or 0 is representable, so, 1+1 equals the highest possible output, 1.The plus (+) symbol in Boolean terms means OR, not to add. Example: A + B = Y means input A OR input B equals Y (the output). A circled plus symbol will denote an exclusive (OR or NOR).
..the instructor marked the answer wrong because the answer is wrong. Even if the macrons were present on (AB) and (CD), because the whole this is NORed, not ORed...In my opinion, your instructor marked your answer wrong because you forgot to include the macrons over AB and CD in your answer for the input to the NOR gate. AB NOT + CD NOT = Y
is this (AB) NOT or is it A(B) NOT ?AB NOT + CD NOT equals Y.
Sorry, if that came across a bit harsh (that wasn't the intention), I was trying to clarify some points I felt could trip up a newcomer....I understand the attention to detail. Notwithstanding how I tried to explain the problem, the point is the student forgot to include the macron in the answer.
But, as you say, it is a NOR gate in the schematic, so the answer would be (using your notation):In my opinion, your instructor marked your answer wrong because you forgot to include the macrons over AB and CD in your answer for the input to the NOR gate. AB NOT + CD NOT = Y
I'm going to have to disagree on this one. Binary addition in an N-bit world is normal addition reduced modulo 2^N. So 1-bit addition is a mod-2 world making 1+1=0. Binary addition is an XOR gate (and, it turns out, is indistinguishable from subtraction, which is a very useful property in cryptography and coding theory).This is addition, however, it isn't decimal addition. This is binary addition, where only 1 or 0 is representable, so, 1+1 equals the highest possible output, 1.
True. I should have specified that I meant a binary magnitude addition(the signal can only take two magnitudes). Adding 5V and 5V can't exceed the 5V supply, so the maximum it can output is 5V. 10V extends past the supply, and 0V wouldn't make sense. A carry in a magnitude simply doesn't exist, so 5V must be the output.I'm going to have to disagree on this one. Binary addition in an N-bit world is normal addition reduced modulo 2^N. So 1-bit addition is a mod-2 world making 1+1=0. Binary addition is an XOR gate (and, it turns out, is indistinguishable from subtraction, which is a very useful property in cryptography and coding theory).
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by Jake Hertz
by Rushi Patel